It's relatively simple, but there are alot of factors involved. As Studio said, since you are new, you will be expected to ship first for a while, until you build up a reputation. Some people will be lenient and ship at the same time though, it just depends on who your dealing with.
A few good rules of thumb to remember are:
-Once you have agreed to a trade with someone, and have gone as far as trading addresses, don't change your mind and back out. It's considered very rude. You can always talk to the other party about it if your having misgivings though, most people are very pleasant to deal with on here.
-
In my opinion, everyone should ship USPS priority with delivery confirmation at the very least. It only cost five bucks, and is VERY reliable. Usually taking only 2-3 days to arrive.
Though First Class is a good option too. No matter what, i think you should always use delivery comfirmation.
-When you box the yoyo up, take care to wrap it snugly, that way when its en route, its safe inside the box, not bouncing around and getting new scratches.
What i usually do is; Unscrew the yoyo and wrap each half separately in bubble wrap. Then take the bearing and axle and put them in a small baggie and tape it to the inside of the box. This ensures no parts will get lost and everything will arrive in the condition you sent it.
I must warn you though, trading is
addictive once you get going with it. It's really an awesome system. It allows you to try all kinds of new stuff without ever having to spend much money. You gain friends, experience, new yoyos, and fun. What's to lose?
I haven't bought a new yoyo (with a few small exceptions

) since i started trading, and i have probably tried hundreds of new ones. Personally i prefer to get new yoyos in trade than purchase them. That is, unless i'm in Eugene

hehe.
All in all, trading is a very very good time. Just treat people the way you expect to be treated and you will have a blast!!
Good luck!!