Draven's Skill Max Order: Q → W → E
Level 1: Draven had the edge level 1, so start Q and only trade if you land blind on him first. This is one of the few matchups where you have to contest for level 2 first, so try your best to get 2 first.
Level 2: If you get 2 first, instantly jump on him for a huge trade. Otherwise, be careful of your E usage because Draven E can cancel your E entirely, which will render you useless. Be careful of him starting W too, because he can run you down. Stay back and see which ability he levels.
Level 3: You must land blind on him or else he can run you down and kill you, so save your Q if you can because if you miss it or use it on the wave, a good Draven will instantly engage on you. Ideally let him E you first before you E so that you can get the slow off of him when he's trying to engage.
Level 6: The lane gets a bit more scary, but the way you play the lane is the same. Play for short trades with your Q, and only commit to a trade if you know you can kill him in an all-in. You outscale, so don't force anything if it isn't necessary.
Draven is tough, but one of the easier ADCs compared to others.
Draven wins all long trades, but you win short trades with your blind.
How to play the trades is to Q Draven, and if you land it, go for a trade before backing off.
Draven E can cancel your E, so be careful about using it.
If I blind Draven, he will likely use E in front, so walk to the side when blinded to avoid it.
You can use E after his Q nearsight expires to slow him when it ends.
Draven is easier to land Q on because he will always try to pick up Axes, so throw Q where his axes are about to land.
Pushing for level 2 first is huge in this matchup, and remember that going even is a big win for you.
If you get 1-2 items, you can destroy Draven in all 1v1s because now you have enough damage to kill him in his blind.
Even if you're behind in lane, 1-2 items is all you need to kill him when he is blinded later on in the game.