As Draven in lane, u really want to harass the enemy. if you trade one for one its worth if u kill them first, because you get more gold than they do because of your passive and you show them who the boss is. just dont feed a hard scaling champ please. Play agressive, but dont stupid.
And hope that your support has a Brain.

If you leave Lane with a Lead, try to hard carry this game. Destroy all Tier one Towers with your team and try to do drake as fast as possible because you will probably get outscaled (not with Bruiser Draven). You need to Snowball, u dont farm Mininos but Champs.
If you are behind, try to get a pick with a lot of passive stacks so you can get a bit of the gold back that went missing in lane. Playing Draven after a lost Lane and beeing behind is really not fun, so if u cant do damage try to win the game with good macro

In Lategame one Teamfight can decide the whole Game. Dont try to poke with one auto since your not that strong anymore in lategame (Enemys usually have better scaling and a lot of armor). Insteat of playing hard agressive its all about beeing carefull now. But when the moment comes, its your time to shine. Also dont forget that you can sell your boots for Youmuu's.

I bet a lot of you guys think this build is pure trolling but it is not. If you play Bruiser build, your autos will do less damage, but you can get more autos on the enemys because you can survive much longer in a fight. Just dont expect to do damage till lategame or till you have 3-4 items. But as soon as you hit that, you are actually a 1v9 machine and you can finally fight all the champs that you wouldnt be able to normally, such as Camille, Tahm, Jax, etc. I go this build everytime i play a game that is not playable as normal adc (enemyteam is full tank and/or Bruiser)
If you have that Trinity + blade + Lord dominiks damage, that stuff will hurt even the tankiest one. Add a got Deaths Dance for more damage and good sustaint or/and Maw and you will not die. Last item is just something you like, maybe GA or Bloodthirster for more heal, you can also go black cleaver since you can stack it because you can fight so long. I never build berserkers because you will get more than enough AS through Lethatl tempo + Trinity + Blade.

optimally you get a serrated dirk or a vampiric scepter with your frst back. You can choose to rush Essence Reaver or your mythic item.
I just love the Essence Reaver rush since you wont have mana problems anymore and you get some nice damage too. For mythics you usually go Shieldbow or Eclipse.
I played with Galeforce a lot but since they nerfed the cooldown of it its not my go to anymore and Kraken actually feels good, obv you take it most common in games against armor stacking.
If they are really Squishy you may go Prowlers or duskblade, but these two items are not the best against armor.
Depending on your matchup Rapid Firecannon may be a good option since you can attack them from larger range (for example against Annie this is good since her abilities are very short ranged and with Rapid you can attack her without getting in her range)