Tank: Obviously enough, soak damage. Initiate a fight, draw as much aggro as possible and PROTECT YOUR CARRIES. I see time and time and time again a tank chasing a low health enemy leaving his team behind to get caught and murdered. Don't ever chase as a tank. Killing people or running down escapees is not your job. Your job is to protect the people that made them hurty in the first place. When I tank, I am CONSTANTLY switching targets, dumping as much damage, CC, and debuffs on the enemy team as I can. If they focus me down and I die, it's usually just fine because as the world turns grey, I hear "an enemy has been slain" "an enemy has been slain" "an enemy has been slain", etc. I don't build stack items on any tank except Galio, because I expect to die as a tank if it means my team gets a lot of kills or an ace. Sacrifice is the name of the game of the tank. If you happen to jungle tank (Skarner, Lee Sin, etc), then ganks are an integral part of early and mid game. Even if it's just a positional gank (as in, come into the lane, do some damage to the dude, but not balls-to-the-walls-trying-for-a-kill), it causes the enemy team to either buy wards, costing them some scratch, or be super skittish and easy to zone. When you have the abilities, time your ganks with AP Mid or Solo Top so that it's a 3-4 man gank. Also, be able to tank turrets so your team can dive and get kills. Often on Skarner, I will ult someone, drag them into my team, and once that kill is secured, I'll pop my shield and just go into the turret, drawing turret aggro so the enemy team has to either jump on me (enabling our dps to dump on one of them), or drop back (enabling our dps to down the turret).
Solo Top: Solo Top is the other mano e mano lane. It's you against the other team's bruiser usually. The goal here, just like AP Mid, is to out-farm, out-position, and out-harass the other teams bruiser. I often have my jungler ward my river bush on top on his way to steal enemy golems, gank top, or grab our blue. It's part of the usual route of most junglers and 1 ward is half the price of 2 for mid bushes. When the laning phase is over, Solo Top, aka Bruisers, have one job: Get the enemy AD Carry out of the fight. If you can gap close and kill their AD Carry, you have probably won the fight and potentially the game for your team. Mobility, Armor/MR, and Health are a must have on a bruiser because the AD Carry, AP Mid (burst), and Tank know you are coming for their AD Carry, so Solo Tops generally get CC focused pretty damn fast. If you can out-position their defensive line and get to the AD Carry, most of them are squishy with weak escape mechanics and will tend to tuck tail and haul ass. Even if you don't kill them, you've done your job. Turn back to the fight and lay down the law. If the AD Carry comes back, chase them off again. Renekton is a god in this role because of his gap closer, stun, ridiculous "tanky dps" builds. Jax is another pain in the ass.
Support: Support is a fairly easy one. Rune GP5, Mastery GP5, keep your AD Carry healthy, wealthy, and gay! Depending on the support you are going with, harassing the enemy teams AD Carry is a must as well. Remember to help your AD Carry focus on farming minions by warding EVERYWHERE and keeping your eyes peeled on the minimap. You are his eyes and ears so he can just lock in on last hitting minions. If you don't warn him of danger or harass their AD Carry, your guy could and will fall behind, and this is bad for your team. I'll edit and add more to this section, but Tansen just invited me to a game! XD[hr:30g6ctqu][/hr:30g6ctqu]
Second Post: Team Fights.
Team fights are when your team decides it would be beneficial to engage the enemy. Team fights should ONLY happen when you have some kind of advantage, whether it's under a friendly turret, the enemy is trying to baron, they are down a man, or you have just dominated them in kills and farm and have much more complete builds. A lot of the games I've lost have been not because I failed in my particular role, but because teamfights happened when my team was at a disadvantage. This is basically the cardinal rule of LoL. Don't fight if you aren't guaranteed of a win. Fair play or equal footing is good on the playground or ball field, but there's no place for chivalry in LoL. One of the creeds I've adopted when playing with RL friends is that there are no hero's in LoL. A hero is another word for suiciding feeder. Don't be "that guy".
Also, don't chase low health people if a full health guy is wailing on you. I see this in almost EVERY game. Your team gets the advantage in a team fight, you get a kill or two, and a guy is low health and takes off. It's like a pack of dogs after a cat, all the while the rest of the hurt guys team is pouring on the dps. Which brings up another great point. If the enemy team makes this mistake, don't just run away too. Pour on the dps. 1 of 2 things will happen: either your friend that is booking it will get caught and die (in which case, during the merry chase, someone on the enemy team was getting corn-dogged with damage), or the chasing enemies will realize they are taking damage and not really gaining an advantage, which means they will stop chasing and turn to address the new threat. You just saved your friends life.
I had this happen in a game just the other day where the enemy team was doing dragon. We saw it, went to go steal it, and I was caught alone on the south side of dragon, while my team was coming from north of dragon. 3 enemy team members started chasing me and I initially started south, away from the enemy and my own team. When it was apparent I was not going to live, I used my escape mechanism (I was Cait at the time) to close the distance with the enemy champs and, in essence, ran through them. In so doing, I brought them to my team who was rolling in like a truck, and with the enemy team's focus completely on me, my team was able to initiate a fight properly. I went down, but we ended up acing the enemy team and I think lost only one other person from our team. Don't be afraid to die if it's unavoidable. My friend Critic, who is a damn good player, always tells me "Don't panic. If they kill you, they kill you, but we'll punish them for it", which is a great creed. If you are going to get dove, lay down whatever CC you can on the turrets target and make them hurt for diving.
DON'T PANIC. Even in a Charlie Foxtrot teamfight, remember your role and do it the best you can, even if you have no chance of living through the exchange. Do your job and have faith that your teammates will do theirs.