Harassment and Lane Dominance

Harassing with Draven is quite easy but the hard part is doing it right. This means you should do it in a way it's hard for your enemy to retaliate and, even more important, from a position such that the enemy support won't be able to lock you down with CC. A second part is to make sure you move that your axe will be easy to catch. You have to 'lead' them. This means that you should walk back before your Spinning Axe impacts so you can catch it on your way out.

To Catch or Not To Catch?

It's not always wise to go out there and catch an axe as the marker where your axe will land is also visible to the enemy team and basically means "Aim your skillshots here.". Spinning Axes which will put you in a bad position aren't worth catching it, especially if Spinning Axe isn't on cool down. When chasing with Blood Rush, however, it's often better to slow down a little to catch the axe rather than to rush past the marker as your Blood Rush will not refresh which means that you cannot use it to continue the pursuit or use it to quickly disengage in case you just overextended.

Proper Usage of Stand Aside

Stand Aside has multiple uses: Mastering the first two is of utmost importance as it allows you to save yourself from ganks and enemies closing in on you. You need to keep your enemies at a distance so you can actually defeat them. The last one is learnt through proper timing in duels with other AD carries and it is a trick that comes in handy.

Whirling Death

When you just start playing Draven, you'll probably not have much feeling for this ultimate. It doesn't feel as if it's part of his skillset and that probably leads to confusion. Whirling Death is basically used to burst at the start of a fight, picking off fleeing enemies or to steal objectives. When duelling it's often smart to save Whirling Death in case they Flash away when on low health though you might need it to actually win the duel. Also, keep in mind that the ability is global so you can use it to aid allies in a fight. The additional physical damage might just be what they are needing in order to win their skirmish.

Juggling Two Axes

Juggling two axes can be very tricky but is very rewarding and a necessary skill to possess if you want to play Draven at a higher level. Practicing on minion waves most certainly helps you with that and allows you to push quickly as well. Always use two axes when duelling or taking down objectives. Try to keep them up during teamfights.