Well, one thing simple : Dont attack champions when they are at their tower unless you know you will survive and run away from it. Towers does alot of damage and with the other champion, it can hurt. Unless you got crasy stats, making you able to tank the hits, its usually a bad idea.
Other thing: Be carefull of junglers. These people pass from place to place in the map, attacking anyone in a gank when they can and know they can survive. Usually when you know a junglers coming, its better to back away.
Also: If you are a mage, watch your mana. Its usually better to keep it for when real fights begin, but still you can use it a bit. Just keep a good amount in all time. A mage with no mana does not do too much damage, with some exeptions (ex: Nidalee's tiger mode dont use mana, but she is a kinda mage.)
I am trying to think of anything else, but for now, that about it. Try learning each champion move to be carefull and learn what each does. The more you know the skills of each champions and their concequences, the better.
Good luck. Hope that helped. I am not 100% sure of everything, but I think its good.