1. Ask about the loot rules. You should ask the party leader about the loot rules ASAP. Yes, most of the time it will be need or greed, but sometimes it isn't, and I guarantee someone else in the group is wondering about the rules as well. It never hurts to ask, and by speaking up you will be 100% sure what to do when the loot roll boxes pop up. Sometimes groups will choose to go with Master Looter on bosses instead of rolling, and this should be established before you enter the instance.
2. BOE Items. Most items that drop off of the trash (non-boss) mobs will be Bind on Equip. What that means is even if you win the roll on that item, you are still free to trade it to others or sell it in the auction house. BOE loot windows are gray in color and will not prompt you after you roll to confirm that you really want to roll on the item. If you happen to win something that someone else in your party claims to need, it is good form to let them have the item. Whatever small amount of gold (or in the lower levels, silver) that you might receive by keeping the item will not be worth the bad reputation you will gain by hoarding loot.
3. BOP Items. Most of the items that drop off of bosses will be Bind on Pickup. This means that once you pick up the loot, you cannot trade it or sell it on the auction house. You will notice that BOP loot has a gold roll box, and it will prompt you after you select need, informing you of the BOP status of the loot. If you are paying attention you should never mistakenly roll on BOP items. Remember, if you see the gold roll box pop up, take a few seconds before you hit need, and review the loot to make sure it is something you really want. Once you loot a BOP item there is no going back.
4. Wait to loot. Never loot a corpse in the middle of a fight. It is distracting to see roll boxes pop up in battle, especially if you are the healer or main tank, who have a lot more to worry about in instances than DPS classes. Additionally, people tend to make more rolling errors when they are just trying to clear a loot box off their screen so they can continue the fight. Just wait for the fighting to end, and while the mana classes are drinking, go ahead and loot.
5. Don't Be Greedy! If you notice you are going on a run where you have won 2 or 3 greens in a row, it might not be a bad idea to pass on a few items to let others get some loot as well. People in your party will appreciate it. Also, if you have already won a couple cloth blues from the instance, it might be nice to allow that mage you came with to grab the caster dagger that just dropped.
6. Just because you can use it doesn't mean you need it. Whoa! It's a blue robe! It has +20 spirit on it. You are a warlock. You don't need this robe! Spirit is a fairly useless warlock stat, and the priest in your group would appreciate you passing. Make sure you do a little research on what stats are good for your class beforehand. Check out the class forums on the official WoW boards, or WoWWiki, if you have any questions on what stats are best for your class.
If you follow these simple rules, you will be invited back for more instance fun. The people you meet at level 20 are the same people you will bump into again and again on your path to 60. You will be upgrading loot so quickly at these lower levels that it really pays to play it cool and try to make some friends via the loot process, rather than snag all the loot you can. As I have said before, just be a good WoW citizen, and you will find that getting groups and finding the proper guild will be an easy process.
Are there any other pieces of looting advice the WoW vets can bestow upon the new guys?