I'm assuming you're in the US. If not, most of what I say here is not applicable. Sorry.
There are a number of variables here. I've done some freelancing, though it was always as a sideline to a "regular" job. Is freelancing your only income or is it a sideline? Have you created a corporation or a limited liability company, or are you doing this as a sole proprietor? As you're asking "newbie" questions, I'll assume you haven't done all the paperwork to create a corporation or LLC.
Regardless of any of the above, you still file taxes once a year, just like you're used to.
If you're a sole proprietor, you'll report the freelance income on a Schedule C. (There are different forms for corporations and LLCs.) This can be an addition to income from a regular job, or it can be your only income.
There's a box on the 1040 to report schedule C income and add it in to your total income. Then you calculate taxes normally, based on your total income from all sources: a regular job, freelancing, capital gains, whatever.
If the freelancing income is small compared to your regular job, you can just add the schedule C to your tax return, and this will reduce your refund or add to how much you owe.
If the freelance income is your only income or is large compared to your regular job, then you have to make quarterly estimated payments. Basically, you have to make a guess at how much money you will make, calculate the tax on this, and then send the government 1/4 of this amount every 3 months. It's the same idea as withholding from a paycheck from a regular job, except that you're withholding from yourself. Then at the end of the year you file your return, and if your estimate was wrong you'll owe more money or get a refund. So it basically doesn't matter if your estimate is off a little. It will all get straightened out when you file your return. However, you can't estimate way low. If your estimate is too low, you'll have to pay penalties. There's a penalty if your estimated payments are, (a) Less than 90% of what you owe; and (b) At least $1000 less than what you owe; and (c) Less than what you owed last year. (https://www.irs.gov/businesses/small-businesses-self-employed/estimated-taxes)
I am not aware of any rule about only paying taxes on earnings over $400. There is no place on any form I've ever seen that says "subtract first $400". If your freelance earnings are small, like somebody paid you $50 for a one-shot job, it's probably technically taxable income but nobody cares. The IRS isn't going to come after you because you failed to declare $50 of miscellaneous income. Clients are in some cases required to send you a 1099 if they pay you over $600, maybe that's what you heard about. But legally, all your freelance income is taxable. Well, I should say profits from freelance work are taxable. You can deduct expenses from income. But see the forms and instructions: there are lots of rules about what you can deduct and when and how. Just because you think of something as a business expense doesn't mean the IRS recognizes it as a business expense.
Yes, you can file electronically. If you've previously filed taxes electronically, it's done exactly the same way. The only difference is that you now have a schedule C added to your taxes, and possibly additional related forms. If the method you've used to file taxes in the past doesn't handle schedule C income, then you'll have to get different software. There are plenty of software packages out there that support a schedule C. I've been using H&R Block for years, I used TurboTax before that, I'm sure there are others. Maybe the free web sites don't support it.