In 57 pages I'm sure someone MUST have posted this already, but I'm stuffed if I'm going to comb through looking for it:
Whatever: Don't make really stupid, predictable, OBVIOUS mistakes.
This may seem obvious, but of course, that's the entire ****ing point. One game I had recently saw me laning with an Udyr who was, not to put too fine a point on it, a ****ing moron. We found ourselves matched up against Taric and Brand, a VERY nasty combo who could hand us our asses in 3 seconds flat just by landing a Dazzle and letting Brand unload. I was cautious and tried to make sure I was never in nuke range of both of them at the same time, but Udyr copped a blast early on, dropping him to about 15% HP. Obviously, I advised him to go back. Predictably, being a moron, he completely ignored me and continued to hang out trying to farm and, equally predictably, he got stunned, nuked and blown to kingdom come the next time the enemy cooldowns were up, giving up first blood and making an already difficult lane practically impossible. Things only got worse from there on out.
In short, don't do REALLY OBVIOUSLY MORONIC THINGS. If you're on low HP in a lane against enemies specialising in burst damage, DON'T hang your dumb ass out to offer them free gold! If half of enemy team has been mia for the last 30 seconds, DON'T decide this is a tactful time to try and solo dragon, especially if it isn't warded. DON'T solo chase a fleeing enemy out of your jungle and into theirs when you have no idea where the rest of his teammates are, because that ****er is pinging like mad for a rescue. DON'T use powerful AoE ultimates (eg. Cannon Barrage, Curse of the Sad Mummy, Hemoplague) to steal a kill on a single enemy champion unless that champion's death is really important to the team or it will secure you an ace. DON'T think you can hold a turret with less that 200 HP left against 3 enemy champs and a double wave of minions when you yourself are almost dead and running low on mana. In short, DON'T BE ****ING STUPID. It may seem obvious, but it's ****ing AMAZING how often people apparently leave their brains on the shelf when they log in. Be good to your brain. Let it share in the fun. Brains enjoy LoL too.