I have had pretty strong success lately following close to this build...I know a lot of vaynes push for a Trinity Build, but i honeslty avoid it on its too costly and not enough dmg in my opinion.
Start with a Doran's Blade, simple cheap effective dmg at the beginning.
I then grab zerker greaves for the attack speed, faster bolts.
If you not getting easy farm at this point or you have been unsuccessful at snagging a kill or two, a cheap way to make sure you don't completely fall behind is to grab another doran's.
If you are ahead on farm or at least kills you should be able to start rushing your first big item.
I always rush a cleaver as fast as possible. the armor pen just stacks so nicely with everything and the extra dmg will rip squishies quickly at this point.
Next start building your first phantom. Zeal first of course. If you don't have all the gold to build the full thing quickly, before you finish it off go ahead and grab a vamp scepter before finishing.
So at this point you should have a Doran's blade, Zerker Greaves, Black Cleaver, Phantom, Vamp Scept.
You should be doing some mean dmg at the very least to casters. You can effectively bring tank health down, but watch CCs. Your job is not to rush in the middle of everything. You have to let your team fights get initiated by everyone else, while you stick to the edges of the group and focus their carry or other casters. I run the zerkers for the dmg, i hardly ever pick up treads just on the fact that you should never find yourself being super close to most CC ranges.
If the game continues on go ahead and farm up your next BF sword and try to finish your Blood Thirster. At this point you should be able to farm stacks pretty quickly before you have to go into another fight. It is noted you may start being coming peoples focus pretty quickly especially if you are doing well at this point so the extra life steal will help.
After BT, sell your blade and push as fast as you can for another Phantom. The increase attack speed and movement speed will become extremely deadly to melting down health at this point. You may even be able to melt tank health down pretty effectively too. (keep in mind if they have a thornmail that you need to watch your health)
Most games at this point are generally wrapping up if not over. Assuming your team has done their job to help push and initiate properly that is.
If you find yourself in a game that will not end at this point your last item is solely up to you and what your needs are. I typically just go all out on the remainder of the dmg scale and push an IE. At this point you will be completely feared. A G.A here can be just as effective especially if you got a few people low, or the other team waisted all their cooldowns on you, and your team is still fighting.
So to recap TLR
My build I have seen strong success in is this:
Sell Blade Rush another Phantom>
Inifinity Edge or G.A