I don't know a lot about paper checks because I have never seen one, and I don't live in America.
Suppose person A gives person B a check for $100,000 in payment for something in a shop. How can B be sure that A has enough money in the bank account to cover the check amount, and is not scamming?
How is this known now, and how was it known before use of computers in banking?
The bottom line is you don't.
Checks are rarely written for that amount, currently the average checking balance in the US today is around $6,000 or so. Traditionally, checks were written for much smaller amounts. Perhaps $200 at the grocery store, $100 at the restaurants, $50 at other merchants.
Many business would black list those that wrote bad checks.
Checks have decreased in frequency because of problems for both sides of the transaction.
However, in larger transactions one can have a "guaranteed" checks, often known as a bank, cashier's, or teller check. In that case the bank would withdraw the money ahead of time from the payor, issue a check, and that payor could then give the check to the payee. Those kinds of transactions happen with home purchases and the like.
In the UK, in the 1980s, if you wrote a cheque to the seller of an item and didn't have the money in your account, the bank would bounce the cheque (and charge you a fee) but the seller would have lost their money and their item.
To give slightly more protection to the seller we had the concept of a "cheque guarantee card" - which looked like an ATM card (and was often the same actual physical card once ATMs became a thing) and the seller would ask to see your card, typically for purchases up to £50 or £100 (depending on the amount specified by the card). They would then write your card details on the back of the cheque and also your address. If you paid for something with a cheque and gave the seller your cheque card details, the bank would honour the cheque even if your account couldn't cover it (protecting the seller), and then pursue you for the money if you didn't have enough.
The "bank cheque" or "cashier's cheque" mentioned in the earlier answer https://money.stackexchange.com/a/95893/739 is one further step up in protection for the seller.
There is a good overview of the history of payment cards in the UK at http://www.theukcardsassociation.org.uk/history_of_cards/index.asp, specifically see:
1969
UK domestic cheque guarantee scheme is established.
...
1989
£100 and £250 UK cheque guarantee limits introduced.
It was also common to call the bank and ask if funds were available.
It was legitimate to call the number printed on the front of the check and say, "Hi, I have this check for $300 from Artem, account number 1139391874. Is it good?"
The bank would either verify funds or say that no, that check would bounce.
In addition to the other answers, there were people that relied on the delay of cheque settlement - you could make a purchase with cheque on Thursday, get paid in cash on Friday, put the money in the bank and it would cover the cheque next week when it cleared.
It was also possible to "post-date" cheques, with a date in the future. This was supposed to defer it until that date, but this wasn't something that banks would always honour.
For very large payments, there are "banker's drafts", which are pre-cleared. The bank effectively takes the money out of the sender's account on issuing the cheque.
Lots of answers, but none that focuses on the example presented by the original poster:
Suppose there is person A who gives another person B a check for $100,000 in exchange for something expensive in a shop. How can B be sure that A has the money and it's not a scam?
Anyone spending $100,000 much who wants something “Now!” yet they cannot provide cash, credit or a cashier’s check (bank check) is attempting to scam someone. Or they are insane; same difference as far as my personal liability goes.
And based on that fact, you need to understand where credit comes from: Reputation. If you have a solid financial record and have little to no debt, guess what? You have good credit! The fact you pay your debts is the reason a company will then allow you to purchase things on credit.
Now if you are a small merchant? Others have discussed this, but unless you are really hard up for cash, you will not risk bouncing checks for small amounts. The long term damage to your financial stability is much more risky than the amount you might be able to “con” away from a scam like this.
The simple answer is that you don't know that you'd get paid, just as you don't know that you won't get mugged and have your cash stolen, or have someone steal your credit card and run up a bunch of charges. But all these things are crimes (in the US, at least), and someone who does them faces the prospect of fines and possible prison time. (With checks, if it's just accidental, you'd only get a significant "bad check" fee from your bank...) As others have mentioned, for large sums there are things like cashiers' checks that are guaranteed. Though people do occasionally write fairly large personal checks, e.g. this one for a divorce settlement: http://money.cnn.com/2015/01/09/luxury/billionaire-divorce-check-cashed/index.html
Really, it just comes down to the fact that most people are fairly honest - either inherently, or because they recognize the consequences of dishonesty. Credit cards really aren't much different: I could easily run up $100K or so in credit card purchases, then just not bother to pay the bills. Though I think it would be the card issuer that would suffer the loss, not the merchant.
There are still countries using cheques today; they are still common in France for example, and every time I've gone to the supermarket there I've seen people (generally older) using cheques to pay.
There is generally no guarantee for the vendor, when paid with a cheque, thought they have a few recourses:
I would note that cash has similar issues (counterfeit money), yet is still accepted in most places. And while credit cards are more secure, they incur vendor fees.
Bouncing a check is a crime. When buying merchandise at retail, the retailer will swear out a complaint! Even for a little one, lest word get around that they don't enforce. First time, a cop will call you and say "settle this today or else". Third time, they won't call, they will put out a warrant and you are a fugitive. You are going to jail.
That... Is why the retailer wanted your driver license number. So he could put it on the police blotter.
If you're thinking "my atm card declines all the time, I'd bounce checks that often!" No. The checkbook has a check register where you log each check, debit and deposit, so you always knew what you had. Auto-debits didn't exist, so they weren't throwing grenades into your checkbook.
If you bounced one, the bank would call, you'd contact the seller and got in front of it. It's what you did.
Also in my day, 95% of checks were to pay mailed bills like the electric bill, where you already have a limited line of credit. In those cases, they choose not to treat it as a crime, just a failed payment. Make another payment by the due date, you are golden except for the bounced check fee. Otherwise the normal late fee also applies.
Don't underestimate the importance of the fact that check law has been maturing for 200 years. The law ( police, courts, civil litigation ) know exactly what to do with paper check fraud of every kind. They've seen it all. They know when it's a crime, who to blame, and who carries liability. In particular, hundreds of years of case law - it's unlikely for any "new case law" to be developed around paper checks simply because everything that could happen has happened. Contrast to electronic payments case law, which is only now starting to be written, and things like Experi-Metal v. Comerica can suddenly change the game.
The world was a bit smaller and most check transactions were small and/or with "regulars" - people the retailers knew. And retailers sized up whether they'd take a check on that basis. Wasn't always fair.
But yeah. We have taken 5 digit checks from people we knew, and knew the transaction was typical for them. Springfield ISD wants another $50k of Macs, okay... Green Hills Country Club, no way.
There were many ways, but in the end, you don't actually know.
You said "without computers", but the general case with them is still interesting.
In the US, since 2004, there is a system called Check 21 that allows businesses (and maybe individuals?) to scan and instantly process checks, in much the same way that debit transactions are processed. This alleviates most, but not all, of the types of issues you are worried about.
UK: Our window cleaner still gets a cheque. He doesn’t know if we have the money, but he knows where we live.
In Germany, cheques were usually guaranteed by the bank up to 400 DM per cheque. Cheques fell out of use around 2000.
For transactions involving transfer of valuable assets and a lot of money, such as real estate, a process known as "escrow" is used. Escrow is a process where a disinterested third party, who is paid for their services, collects all the documentation and money from both the buyer and the seller, holds it until it's shown that everything necessary has been delivered, signed, etc, and then delivers the money to the seller, gives the deed and any other necessary documentation to the buyer, notifies the governmental agency which records property transfers, etc, etc, so that the property is properly transferred, the seller is paid, and so forth. When it comes to transactions such as these there is actually very little "trust" involved - the escrow process which has been developed over many, many years has replaced "trust" with procedures which are intended to guarantee that the transaction is completed properly.
How did people deal with checks before computers and other things that made it easier to verify?
The same way they handled the precursors to checks, which were promises to pay. Kind of like running a tab at the bar, that privilege is reserved for trusted parties or those so well known that the hit to their reputation would be more damaging financially than the amount being floated.
Imagine you live in a area where everyone knows where everyone else lives. We know your address, what job you have, and roughly how well you're doing financially. There's no such thing as checks. You stop by the store, want to purchase some items and won't be coming into "town" for another week, but aren't carrying negotiable instruments with you and don't have the time to get them for the purchase now. What happens? Well, if you're well known, with strong ties to the community, and have been honest in your dealings in the past, and the store can tolerate not having payment for a week or two, the store may decide to record your debt in their books with the expectation that you'd pay it later. If you didn't pay, you may expect a visit later from the authorities or you'd find yourself blacklisted not only from the merchant you stiffed, but using such services at a wide range of other merchants.
So, given that you need to live and trade with these people, you are established in the community, moving somewhere new would be problematic, not to mention much more expensive than whatever it was you wanted to buy, why would you skip out on the debt? Or even take it on if you had a strong likelihood of not being able to cover it?
But this system is problematic. It requires you to physically come back to the town with the money (potentially dangerous) or go to the bank, withdraw the funds, then pay the merchant (time consuming). And the merchant is essentially giving everyone who takes advantage of this an interest free short term loan (not necessarily good business).
The next month, the banks announce a new innovation - the "check". Which is now a piece of paper that when presented to the bank, results in a transfer of funds from the payer's account to the payee's. This reduces the amount of time the merchant needs to float funds from days/weeks/more to just business days. This removes the need for the customer to return to town, which saves them time. But it changes nothing else. You still only conduct such transactions with people you trust or people you can leverage into paying up.
If anything, the ability to defer trust to an electronic system is likely what enabled even more fraud. Since you don't need to exploit personal connections and trust, the threshold to scam someone is much lower.
So, TLDR - this worked due to tight communities and some amount of trust which predates the invention of checks. For you to pass a fake check, you needed to be able to execute a confidence scam - convincing someone you were trustworthy or person of importance/reputation, or convince someone who already has those qualities to either vouch for you or put up their own money while accepting your worthless check.
You Don't
A personal check can be cashed for up to the amount written on it (so in your example, if the writer of the check had $4,000, you could clean out their account by cashing it, but would not be able to get more than that), but generally speaking, if a check is written for more than the writer has in the account, upon cashing it will 'bounce' and the person cashing the check will not receive anything.
Bouncing a check usually carries a penalty or fee as well as potentially earning yourself a blacklist from certain shops (I falsely assumed that bouncing a check would also hurt your credit, but @ThePhoton set me straight). As an individual receiving a check from another individual, you are essentially out the money, and will have to take legal action to recoup either the money or the item you sold.
As already stated, you don't know in advance if a cheque will clear - it is a paper promise to pay, and is only as good a promise as the customer's word. Vendors will more readily accept cheques when the vendor has recourse of some kind - the goods sold can be readily repossessed (like a car), the tenant can be evicted (apartment etc. rentals), a lien can be placed on the customer's home or car (repairs, etc.), or there is enough time from payment to delivery to cancel the transaction (such as a deposit on a car purchase). Businesses will also accept personal cheques from customers with whom they have had reason to build trust.
Vendors often refuse personal cheques in situations where there would be significant finanacial exposure. They will usually require cashier's cheques, certified cheques or bank drafts (all amount to the same thing) - placing trust in the issuing bank rather than an individual.
Example: I just sold my car privately - I required the buyer to pay by certified cheque or bank draft before I signed over the ownership and handed him the keys. I would have been foolish to accept a personal cheque.
But... if a family member was giving me money for whatever reason - gift, purchase of something, etc., I would accept a personal cheque because of the trust present in the family relationship.
