Graves is an AD Carry (Marksman for the sake of Convenience), who functions somewhat similarly to an ad caster in the early to mid game, due to his extremely powerful burst damage. Recent buffs have helped compensate for his low range, and as a result, he's back in the competitive scene, also thanks to the Lucian nerfs, and is now considered a top tier adc. He's a great pick for solo queue, and can stomp lanes especially once he reaches level 6. Alongside Kalista and Ezreal, he's one of my favorite AD's and is really fun to play. He is not a hypercarry, but he has a great laning phase that can allow him to snowball effectively in the late game.
Max Q first, then, E, lastly W. Put points into R whenever you can. (6,11,16)
You're strongest at this point in the game. If you're with an aggressive support, you can easily pick up first blood with your W-E-Q-R combo. You can use your Q as both a farming tool and harassment tool, but don't use it too often because you have a small mana pool. Play safe against long range AD's such as Caitlyn and Kog.
Unfortunately, your burst falls off late game. If you lost laning phase, then there's not too much you can do besides farm and try to catch up to the enemy ad carry.
Generally at this point in the game, you won't be reliant on your burst in fights, rather, you'll play the role of a traditional ad carry, autoattacking and dealing as much damage as possible.
As I said earlier, Graves is no hypercarry, but is still a good all-around adc, and if you play him right, he can be very good throughout every stage of the game.