For something that's exclusively being handled online Paypal is probably the surest way to get paid, although you could also just have them send you a check. Paypal does take a cut if they use a credit card as the source of funding though, so you'll end up clearing about 3-5% less that way.
Walter's right though - it doesn't matter how you get paid, the government wants a cut! Basically, the way it works is that for amounts under $600 it's up to you to declare the income on your tax return under the 'additional income' section. For amounts over $600 the person paying you is supposed to send you a '1099' - a form for misc non-employee income which basically lists how much they paid you that year. Then you would file that with your return.
In either case you're likely to owe something, although if the amount is low and you have a regular (W2) job as well it'll likely just offset your return slightly.
If the amount is large enough that you'll actually owe much in the way of taxes you'll probably want to file a schedule C as a sole-proprietorship (meaning you're a business, but it's just you). This lets you claim any business expenses (cameras, computers, software, paper & ink, mileage, etc) against the income you made from the video, which will reduce the amount you owe taxes on.
Welcome to the downside of independent contracting, where you get to learn all about exciting topics like accounting, bookkeeping and tax preparation!
