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Maybe it seems a very silly question but I think it is not. I am working as developer for a firm and I have a huge problem to remember and distinguish what the bid and the ask prices are.
I know that the bid is related to the best buy order in the market meaning that if you execute a selling market order you will sell the shares at this price.
What do you use to remember this in a straight forward way? (without realizing all the reasoning that I have made)
Thank you very much
The words are straight forward,
bid is what someone bids for your shares;
ask is what someone asks for his shares, if you care to buy them.
But if the literal interpretation is difficult to remember:
Both of them are a dollar amount. They both refer to the money. The ask is someone asking for money: they are offering to sell. The bid is someone bidding a certain amount of money: they are trying to buy.
Are you familiar with auction terminology? When someone bids on an item, they are offering to buy it for that price. If the person auctioning the item off isn't satisfied with the current bid, they will ask for more.
Suppose the bid is $10 and the ask is $12. All you have to remember is that the bid/ask spread never works in your favour: when you sell, you'll be paid the lower of these prices ($10, the bid) and when you buy you'll pay the higher one ($12, the ask).
First, the bid price is always less than the ask price. You can remember it mnemonically, since the term is named 'bid/ask spread', the bid goes first, hence it is smaller. So the bid/ask spread is always 'positive'.
Second, you should remember that to buy some 'entity' you have to pay more (the ask price) than you would receive from selling the same 'entity' (the bid price) in the same point of time. You are always in a kind of disadvantaged position and pay some comission to the market maker.
To consolidate this idea, as a thought experiment, imagine where would the market makers be today, if they used the 'negative' bid/ask spread and always payed you the commision.
Your Seller Asks.
Your Buyer Bids.
An easy way to remember is to look at the orderbook. 
From an auction perspective, you want someone to lower their asking price (coming down from a high price) when selling to you.
Likewise, when selling your own good, you want people to bid up the price. This means bids go up (and start low), while asks come down (and start high)
A market maker is a designated market participant or a brokerage firm that offers to buy and sell securities at displayed prices on a securities exchange.
As an analogy, think of the market maker as the retail owner of a business. In order to make a profit, he buys at the lower price and marks it up in order to sell at a higher price.
You are the customer. When buying, you pay the higher price. If the market maker is restocking inventory, since he buys at the lower price (wholesale), that is what is available to you as a seller (retail).
If so inclined, you can act as a market maker and post better prices than the market maker but that's Bid/Ask 201.
