I've posted in a number of threads with similar topics that have a fair amount of useful advice. You can find some of those threads here: http://boards.na.leagueoflegends.com/en/c/tips-tricks/nikbT0tA-adc-help-plz
http://boards.na.leagueoflegends.com/en/c/tips-tricks/P7MYF54M-how-do-i-carry-games-as-adc
http://boards.na.leagueoflegends.com/en/c/tips-tricks/rjNKcEER-unbelievbly-bad-at-lol-going-to-quit-if-i-cant-become-decent
http://boards.na.leagueoflegends.com/en/c/tips-tricks/AqBRZdE2-please-help
http://boards.na.leagueoflegends.com/en/c/tips-tricks/dHyAcJoE-help-on-getting-better-at-positioning
I'm an unranked support main who plays ADC as the need arises, usually Varus. Historically I suck at this role, but I've seen a lot of success in recent games. Here's a quick version of my typical advice on playing an ADC marksman:
The ADC plays for the middle and late game, in which their role is to do high, sustained damage in teamfights and, especially, when taking objectives. Despite what the Vayne mains may tell you, your job is not to 1v5 the enemy team and get a pentakill. Rather, your single most important job is to stay alive. Rule one of playing ADC is DON'T DIE. Death in the early game sets back your late game power spike and accelerates that of the (usually) ADC who killed you, while deaths late game take away a lot of your team's capturing power. Since you are playing for the late game, be careful to keep your farm up all game, until you reach your full build. Also, practice auto attack canceling and orb walking (Youtube can tell you what this is).
In lane, your goal is to get as much gold and experience as you can and deny those from your enemy if it is safe to do so. Practice last-hitting and focus on avoiding taking damage. When the opportunity presents itself, go ahead and harass your enemies. If you are
,
, or another early game damage dealer, harass for a little while, then go for a kill and get your snowball rolling, but only if you are sure you can do so safely, without a gank from mid or the jungle. If you are being harassed away from your farm, keep yourself safe and farm under tower as well as you can. Most importantly, don't die. You can't farm experience or gold when you are dead, and you'll just give your opponents a point to snowball from. Unless you want to push hard, it is not usually worth the mana to use your abilities on minions. Save it for the champions and use your powerful auto attacks for farming.
Come mid game, you'll need to start roaming. From this point onward, you will be focused on objective control, and will need to be sure to be around any towers you intend to destroy. Don't be afraid to go out alone and split push or clear a wave that's pushing up against your tower, so long as you have enough vision control that you will have no trouble escaping if enemies try to stop you. I have a history of out-warding my support when I play ADC, as I try to maintain a pink ward at all times, and upgrade my yellow trinket if I expect to spend any time alone. Not only will this make your support happy, but it will keep your death count low. If an enemy does manage to get near you, don't stick around and fight them alone. Head for safe territory and kite them if you can afford to do so. Do not take undue risks.
Wave management is a huge part of playing ADCs, and it is one of the many things that separates decent ADCs from good ADCs. In the laning phase, learn how to efficiently push or freeze lanes while maintaining a good CS (again, Youtube). Let your enemies push near your tower if you need to play safe or want to set up your jungler for a gank. Avoid pushing your lane if you have reason for caution or expect an enemy gank. If you want to create pressure to keep your opponents from defending an objective or joining a fight elsewhere, push hard to their turret. You can also push if your enemies are dead or basing, or if you do not fear a gank. Pushing minions under the enemy turret allows the turret to kill them, denying your opponents last-hit gold. It also gives you an opportunity to harass your opponents without significant retribution, as they will have to choose to return fire on you or to clear the pushing wave. If your enemies are not present to defend the turret, pushing gives you an opportunity to put some damage on it, and gives you a chance to base, as pushing a wave under your enemy's turret will cause their wave to push to near you turret by the time you return to lane, giving you a safe opportunity to farm. If you want to push hard, don't be afraid to ask your support to damage back line minions to accelerate the process.
Team fights are a scary time for ADCs, since you will often be your opponent's primary target. As usual, your big duty is to stay alive. Keep to the back line, ward your flanks, and back off if you are dived on. Kite and let your allies peel for you. Keep auto-attacking any enemy you can reach, preferably the enemy damage dealers, but keep your distance and do not dive into the enemy team, even if that means that the only target you can hit is the tank. You are squishy and they will kill you if you step even if a little out of position. Whatever the outcome of the fight, you need to be alive to properly capitalize on it, taking or defending an objective as necessary.
Finally, be a pleasant person to play with. Praise your allies and opponents for quality play and maintain a good attitude even when things are going poorly. You've played support, so you know how much garbage can be thrown your way by an unfriendly ADC. Sometimes something as little as a well-placed ward is grounds for a compliment, and your support will appreciate that you are acknowledging what they are doing. When you play an ADC, it's easy to think the game is all about you, or that it's up to you to carry it. At the end of the day, all that matters is having fun, and a good attitude is more important than which nexus is destroyed. Stay positive, be friendly, and enjoy your leisure time. Happy farming!