Art Trades are when person A draws something for person B and in exchange person B draws something for person A. Requests are when person A draws something for person B with nothing given in exchange. Points Commissions are when person B pays person A to make them something using deviantART's in house currency: points. Commissions are when person B pays person A to make them something using real money through a service such as paypal. Collaberations are when person A and person B both work together to make one piece. This can also include more than just two people.
All of these, except for points commissions, aren't exclusive to deviantART and can happen anywhere on the internet or real life.
Art trading is basically an art exchange between you and another user. You both agree to draw each other something: a request for a request.
1) Someone proposes an art trade. 2) You both agree to the parameters and theme ("I want you to draw my character; full-body; colored, and I'll do the same for you! Here's a link to her." "Okay! Can you draw me my OC, Blahblahblah?" "Sure!") 3) You draw the artwork. 4) You upload the artwork upon completion. 5) The other person uploads their half. 6) Art trade completed. You leave some love comments and shit about how much you love it.
People don't like it when you scam (e.g., don't complete your trade half), and prefer that you keep them updated on your status if you can't complete it. I know there have been art trades I couldn't complete, so I just pay off the other end as if it were a commission. Some artists are understanding about this, but some have been ditched out on too many times and are a bit wary. Life comes up, but be sure for the most part you can be committed to completing it.