I'm not 100% sure where your confusion lies, but at its most basic, you tell the person how much you'd charge to draw their request, and they either accept it, or don't. Everything else comes down to individual negotiations. There's no 'official commissions process.' But
in general...
- You need a PayPal account, if you don't have one already. There are other options, but it's far and away the most popular. Most of the people asking about commissions will also have one. If your creditors aren't accepting online payments, you can also link your PayPal account directly to your bank account. I believe that is a free service.
- DeviantArt apparently has its own currency in the form of 'points,' but since they're only redeemable on DA, they're not going to be super helpful with your finances. Don't accept BitCoin either.
- It'll speed things up if you decide in advance how much to charge per character/for color vs. black and white/for portraits vs. full body shots etc. Be upfront about content you will or will not draw. How much to actually charge is... idiosyncratic. I can't help you there, but try asking other artists on AOTK or DeviantArt to get a feel for the market.
- Same goes for copyright, but in general most people commissioning this kind of art don't want the actual pen-on-paper illustration. They might specify whether they're okay with you making it viewable on public websites like this one, but shipping costs are probably a non-issue.