Draven is one of the most difficult and rewarding players to play as an AD Carry, your main goal with Draven is to crush your lane and deny farm to you opponent, since i will be working on this guide i will just highlite the most important things:

1.- DRAVEN's NERF.
Since the passive was removed, many players thought that draven was denied most of his powers, what they don't realize is that the new pasive makes Draven a very easily feeding champion, the main rule to a Draven starting the game is to stack your passive, always farm with an axe up or even two if you master the mecanics, you can hit a minion with the spinning axe and move a little bit and hit exactly again when the axe falls down to your hand, almost instantly, with practice.

Done right, with an experienced opponent, you could get 300 from the kill and 300-400 from the passive.
DRAVEN IS A HIGH RISK-HIGH REWARD CHAMPION. if you lose your stacks you are losing gold, you are the only champion able to lose gold.

2.- STAND ASIDE.
It really is draven's main tool at starting fights, saving members of your team, turning a 1vs1 fights, you can interrupt channeling ultimates like Kat's or Nunu's.
And my favorite use: interrupt gap closers at the right time: Shyvanna, Aatrox, Lee Sin, Corki, Jax, all except Vi's ult.

3.- BE AGGRESSIVE.
By minute 2 your opponent ADC should have 1 or 2 axes painted all over his face, the initial burst is the most important in order to take a comfortable aggressive position, Draven's cons like: no having escapes, the nerf and his short range are only compensated by being the most aggressive you can be.

Practice your playstyle and have fun, also try to do the juggling axes when doing Dragon, it just looks nice, Get Draven's ego to yourself, be Draven: the best' is wherever you decide to set the bar each day.