Like, this is a serious question... I make some different types of art in drawings and stuff and some people are offering to pay me for commissioned works online, and I have no freaking clue on how people do things like that. Idk if I can set up balance transfers through my bank account? or other things. I'm kinda wanting to do this since it can help me pay for things in college, etc.
How commissions work is that you earn a certain percentage of the amount of the sale, and this is usually used to pay people in industries such as realty, auto sales, and electronics. Say for example someone sells someone a house for $100,000 and they make a 5% commission, then they would get $5,000 as their salary for selling that house. They can make as much money as long as they keep selling products.
BryanM is correct about commissions with certain types of sales, such as real estate. However, my understanding is the commissioned sale OP is concerned with is with an artist basically getting hired to create something. This is outside my experience; however, I'd say the one critical thing is to Make Sure You Are Paid. Also critical: avoid those pulling scams. For online, I have to wonder--but I only wonder, no actual knowledge--that something like PayPal wouldn't be a standard choice of some.
I haven't done the type of commissions you are talking about, which seem a little less "official" and more like personal art requests. In the industry checks are still pretty standard forms of payment. But if you are getting paid by individuals for sketches and stuff (I've seen a lot of DA artists do this) Paypal seems sufficient. It's safer than giving out your address or bank routing number to a lot of random people, and quicker and simpler than being paid by check.
Not an artist, but I did commission a work from one on Tumblr. I paid through Paypal. I think that's the most common mode of payment for this kind of thing and it allows you to get paid without having to share your bank account information. Then, from there, you can spend the money directly or transfer it to your bank.
In the furry world, it seems like pay-pal tends to be the main method people use to get paid for artwork comissions, as well as writing. I've commissioned a few pics of my fursonas, and used Pay-Pal, and things went well, though I've never been on the receiving end, Money-wise. But in many fandoms involving artwork, a Pay-Pal account seems to be the way to go. Just be sure you get the money and it clears before sending out any art, whether digital or on paper. Hope this helps, ~Simo