Draven, is a very easy champion to pick up, he is quick "OP"(over-powered).
When i started with him I controlled the game! By the end of the game with this build I had massive criticals of 1000 damage!(with this build)
If you follow this build perfectly you will see that you'll be fed easily!

These items are expensive but you'll get fed easily with this build. You should start with boots and three health pots to get the sustain in the lain to farm for a longer time than you opponents.By the time you get to about 2000 or more gold you should go to base and by the vampiric scepter along with the b.f sword. The rest you know.
If the other team only has tanks! you should change the The black cleaver to a Last Whisper for that armor pen.
The frozen mallet seems to be a under used item, the item is really powerful because it gives you health and slows your enemies, because by that point (when you buy the frozen mallet) your enemies will run away as soon as they see you because they know they have no chance!

(If you coming behind them) You should open with your Q and W, as soon at they run away or fight back send out your E and than your R (if necessary)
(if your coming in front of them) Try and open with your E, than get close to them with your W and Q while your getting closer to them, keep attacking if they are winning the engage try and use your R!