I find Caitlyn is an easy ADC to pick up, since she wins most lanes due to her long range.
You don't really want to get involved in fights unless your team is winning it or you have at least four items (including boots). Never go in first, and you usually want to have >20-30 BT stacks before you fight. You can come back from any game if you avoid fights with fed enemies and just farm. If they come for you while you are farming, then you'll have to run. Ezreal is good because you can farm a lane anywhere mid-late game using your ult, and it will be ready when you need it because of it's effectively low CD (due to Q).
Other than that, alot of your early game, around level 5-10 will rely on your support, but don't rage at them if you get blitz-pulled and die. It helps no-one, and they're less likely to help you if they dislike you. Tell him to buy wards, and if he doesn't, you'll have to do it yourself. You get a ward for 3-4 CS, so it's not a major setback to buy 2 whenever you go to lane. If the support buys them, even better.
I find ADCs do lots of damage level 1-7 or 8 from their abilities, like Graves, Varus or Cait.
Don't go in front of the caster minions unless you want to kill. Also, some carries can be aggressive early game; Graves can often kill someone as soon as he hits level 6.
Boots and 3 pots works as good starting items for almost anyone, while some can get doran's blades. It's usually good to get 2-3 blades early, and a vamp. scepter can work wonders for sustain.
Try and work out where it is you are doing badly; are you getting focused in teamfights, is the enemy zoning you, do you get killed whenever you move lanes? And defense is always important; a negatron cloak can stop LeBlanc or Veigar killing you on sight, and builds into a BV if you want. Defense>Offence. I say this because if you just lose, and the other guy was on 100hp when he killed you, defense actually gives you more damage because you last twice as long, up to about 100 armour or MR. A negarton cloak or chain vest on it's own will give you plenty of defense.
That's all I can think of at the moment. I'm not an expert though, so I may be incorrect on some points