There are three lessons I can say about playing ADC in my experience. I call them Farming, Last Whisper, Focusing Your Fire.
Your primary job is to farm. You scale off gold. Learn to do it. I'm not good enough at farming, but if you can reliably last hit 90% of your minions in lane you'll do great.
TL;DR: LAST HIT DANGIT. LAST HITTING A WAVE IS FAR MORE IMPORTANT THEN RUNNING OFF INTO THE JUNGLE TO CHASE A ZAC.
There is basically no time when Last Whisper isn't a good buy for an ADC If I remember right, its only not worth it when they have under 50 armor.
As an example, a level 8 Ashe with no defensive items or masteries towards armor, with just the (pretty much required) 9 armor yellows... has over 50 Armor. And it simply gets better and better as it goes up in level. Some champions like Graves or Miss Fortune can even make a good argument for buying LW as a second item. (Like BT-LW) Most every other ADC will want it immediately after their Zeal.
TL;DR: BUY LAST WHISPER AND DO NOT WAIT UNTIL 30 MINUTES IN TO DO IT. IT'S NOT YOUR "BUILD POLISHER" ITS YOUR CORE.
The other thing you need to worry about is movement in team fights. People will bitch at you for no good reason regarding "STOP FOCUSING THE TANKS" But your job as ADC is to focus whatever you can safely deal damage to.** You aren't focusing the squishies.** You aren't focusing that one guy who's killing everyone. Your job is to attack basically, what is closest. If that fed Jax is beating someone near enough to you to attack, and he just used his leap, auto attack him a bit. Just remember he's going to leap on you if you sit around too long. Always, always move away from combat.
The only reason that Marksmen rule and Melee Carries drool is because of range. You can deal damage without being harmed in return. Remember that. Don't go in if you can't get away. Some carries are extremely good at not dying. Tristana is a fine example of this. Her abilities are all good at making sure she does not die.
TL;DR: YOU HAVE RANGE, USE IT. QUITE OFTEN, YOUR JOB IS IN FACT TO FOCUS THE TANKS WHILE NOT GETTING KILLED BY ASSASSINS.