While there are many extenuating circumstances and different situations that might make some of these statements that will follow not always true, in the vast majority of team fights it is extremely good advice.
Your job in a team fight is obvious, but easier said than done: do as much damage as possible without getting caught/dying. One common problem I see with lower level players is that they think "oh we're supposed to focus the AD carry" so they run in and shoot at the other carry which, because both of their ranges are long, puts you in the dead center of the team fight, right where all those bruisers like Pantheon and Riven like to jump on you and kill you in .3 seconds. Instead of going for their AD carry what you should do is put shots onto whoever you can reach. The only time that you should change targets is when a better one becomes available. An example of this is that if you're shooting Malphite you're not going to do much damage but at least you wont die. Teemo decides to start chasing with Malphite to try to kill you. Since both targets are approximately the same distance away and you won't end up in the middle of the team fight by swapping to him, kill that annoying little boy scout. After which you can go back to shooting Malphite if no better target is presented. The reason that this is good is because of my next piece of advice: sometimes running is better than shooting. The longer you stay alive the more probable it is that your team is going to win a team fight. If you realize that 3+ people are coming straight for your throat don't be a hero and try to life steal your way out of it. It won't work. Run like the little girl you are. This allows the rest of your team to get free damage done while their team chases you around. My last piece of advice is this: If you have trouble positioning yourself in team fights try counting to two when the fight starts, staying back until you reach two. This allows for the enemy team to waste their cooldowns of their spells so that you don't get instantly nuked.
Recap on AD:
- Shoot the best target you can without putting yourself in harm's way.
- Flee if you're in danger.
- Play like a little girl, because you're fragile like one.
Your job is simple: nuke the highest damage threat on their team. This is usually the AD carry or the AP carry, though sometimes it's some wicked fed bruiser. I only have a few pieces of advice for this role in a team fight, the rest seem pretty obvious (PRESS QWER AND KILL THINGS). The biggest piece of advice I can give is to not dump your abilities right away in a team fight. Sure, you might be able to take Lee Sin to half health, but what if instead you just completely killed Soraka before she could even get her ultimate off? That's a lot better in most cases. Another common mistake for lower Elo AP players is the need to stay in the fight poking with your abilities for as long as possible. This is a great habit, don't get me wrong, but if you're 3 bars of HP and your escape ability is on cooldown either just leave or wait for your escape to come back. Have a way out. Lastly, don't dive into the middle of the fight (unless you're Karthus or Kennen or something). It will just get you killed before you can do your job.
Recap on AP:
- You don't always have to dump every ability at the start of the fight.
- Poke with low health only if you have an escape.
- Don't dive into the middle of the fight.
You are your AD carry's little bitch. Follow him around at all times in a team fight. He is the best target to heal, the best target to stun for, the most damage to protect. Sure, if you're Alistar go ahead and engage, but after you engage don't run around chasing kills, you don't do damage. But Jinx sure does. Too bad you let her die to the Warwick that you could have stopped from ulting. Moral: Protect her! The last piece of advice I want to give is simple: Auras are awesome. Having a Frozen Heart, Aegis, and a Talisman of Ascension's is just stupid good. Do it.
Recap on Support:
- You are your AD carry's little bitch.
- Healing the AD carry is more important than healing anyone else.
These are characters like Renekton, Shyvana, Mundo (to state the obvious). Your job is probably the hardest thing to communicate in words. Basically, you are the front like, you are what the enemy sees. You are, generally, the engage for your team. After your engage has happened, you have to make a decision: Do you follow carries to go for kills or do you peel for your team? The reason this is such a big decision is that if you decide to go for their carries that leaves your counterpart to do the same. Whoever got the better engage generally wins this, though certainly not every time. Note that, in general, the person killing you will be the enemy ADC. This is because you are what is standing in between them shooting your squishy teammates. If you can stay alive longer than their tank you'll probably win the fight. Try to position yourself in the center of both teams, because that's what you are, the center of things.
Recap on Bruisers/Tanks:
- Engage and run interference.
- Commit to killing or peeling.
- Center yourself in the fight
These are characters like Talon, Zed, ect. Your job is the easiest yet one of the hardest. Kill. That. Carry. Problem is that if you die before you can do your massive amount of damage to their carry your entire purpose is wasted. Biggest piece of advice is to ignore/run past tanks and the like. Get to the carries and eat them. You can also go Faker on people and assassinate the support. This is good against supports with a massive engage like Annie or Sona, and gives your team a distinct advantage.
Recap on Assassins:
- Don't waste your damage on anyone that you can't burst instantly.
One thing I did not mention: if the enemy is being carried by a caster roles can change, i.e. if your Xerath is just going HAM on bitches but your AD had a hard time in lane and is behind, support's job is now to protect that Xerath to the utmost of their ability. The role would flip for the other side as well, making him the main carry of focus. Keep in mind that this is a general guide to team fighting, since it is not possible to ever put every situation on paper.
Lastly, USE YOUR ACTIVE ITEMS. I personally rebound the 6 key to T, it makes for easier access in my opinion. Shurelia's or Locket can literally be the difference between an ace or killing 3 players.