You want to start B. F. Sword with your first back as the huge +40 AD helps a lot in lane you want to go Vamp Scepter next for the 10% Life Steal which helps a lot with sustain in lane.

Build into.
Deaths Dance will help your burst and sustain late game with the extra 5% Life Steal from the Vamp Scepter, the passive also helps a lot with trading which is really good with Draven considering that he snowballs insanely easy as long as you kill them first. The Statikk Shiv gives you crit as well as it's passive giving you some insane wave clear. The IE utilizes that crit giving you +50% crit damage and also +70 AD.

Boots
Only build berserkers as it is the best offensive boot buy for Draven.

Other Choices
These are just some other choices for the end of your build. The Blood Thirster is really great when your fed and you need to sustain a lot of damage really quickly on-top of the Deaths Dance Life Steal. The Maw of Malmortius is for very AP heavy teams, it is good because it also gives you a bit of AD while building MR. The RFC is for extra crit. The Youmuu's is really good for armor stacking game. Duskblade is for pretty troll games if you want to just take Dark Harvest and one-shot people. BORK is for a mix of everything Draven builds: AD, attack speed and Life Steal, it also has a passive targeting a champion and using it will deal 100 magic damage and slow them for 25% of their Movement Speed. LDR is for tanks with a lot of HP that or teams that are stacking armor because of the armor pen. Mortal Reminder has Grievous Wounds on hit effect too which is good against champs with a lot of life steal... Or Mundo. PD Is for some extra crit and attack speed. and Merc Scimitar is for teams with a lot of CC.

Recommended Final Build
This is my recommended final build as it has all that Draven needs to carry a game. It has the damage from Deaths Dance, Infinity Edge, and Blood Thirster. It has the attack speed from Phantom Dancer and Shiv. The attack speed from Shiv, Berserkers and Phantom Dancer. And the sustain with the Life Steal from Deaths Dance and Blood Thirster.

Old T1 Build
This pays respect to the Draven God Tyler1 this was his old build in previous seasons.

One-Shot Build
This is a build if you want to **** around and just one shot most of their team.

You always want to max Q as it is your main source of damage with it fully leveled your q scales with 105% base attack damage on top of your regular AD. I take E second for the slow that it gives early games which let me cheese a few people early on. The W I max second though because of the better scaling and being able to reactivate it after catching an Axe is really helpful when kiting and adding a lot of DPS because of the improved attack speed.

Press The Attack is really good for Draven as it just gives boosted damage in lane which is what Draven is all about. Triumph is also really good as your passive gives you bonus gold for kills so will Triumph it also gives back 15% of your missing health back which is great for 1v2s, 1v3s etc... Legend: Bloodline is also a really solid option because Life Steal overall is great for Draven as it helps him sustain damage which can help in tough situations and it also scales with his Q. The last one is kind of a tie as all of them can be really strong on Draven but, I take Cut Down for late game as almost everybody in the game has a higher HP than Draven at that point.

For My secondary I take Domination for the taste of blood which adds some pretty solid life steal early game and Eyeball Collection which helps you snowball even more by getting permanent AD on Champ and Ward takedowns.

I will be adding more Matchups as time goes on.