Vayne is great at late game but also she is good at early too. If the late game come she is uncountered. She is very good on harassing, farming and on team fights.By farming well using your abilities smart you can easily carry the game and lead your team to the win. I believe that she is the best ad carry for silver and bronze division. The folowing guide is for ranked games.

I prefer supporters with cc like alistar and leona but I mostly prefer supporters with pulls like thresh or blitzcrank. Taric could be a great supporter for vayne. He stuns the enemy near the wall and then vayne uses her E to stun the target again. I like blitzcrank as support because he pulls the target to the target and I am using Q + E to stun him to the turret and I instant take a kill.

Magic resist runes is optional, depending on enemy team you will judge if you will pick magic resist or attack damage glyphs.Also attack damage glyphs can helps you to farm easier.

Flash: I think this is the most importand spell. You should choose it.
Cleanse : If the enemy bot have players whith crowd controls (for example: Ashe,Leona,Varus etc.) is very usefull. If it is still dificult to escape from their cc build mercurial scimitar. It can also dodge ignite.
If enemy team do not have cc players pick ignite for early game kills or barrier.

Starting items: I always start with boots + pots but if u have problems on farming you can start with doran's blade.

Early game items: Zeal is also a great early item which gives you movment, attack speed and critical strike which are very important in early game.When you have enough gold complete bloodthirster.When you complete it buy statikk shiv for better farming. DO NOT FORGET TO SUPPLY YOURSELF WITH POTS OF HP.
Opitional items:
Blade of the ruined king is a great item against champions which have high hp.
Guardian angel is a great late game item and it can high your chanses to win a teamfight.If its passive is wasted I prefer to sell it and buy warmong's armor or a second bloodthirster.
Statikk Shiv is good on early game to farm well. When you complete your build sell it and buy phantom dancer.
Mercurial Scimitar is an item that you should build if you do not have cleanse.

Full build: If you have enemies with high hp is better to buy blade of ruined king instead of bloodthirster. Warmong's armor is not an essential item. If you win the teamfights easy you can build second bloodthirster or phantom dancer. Warmong's armor hp regen is very helpfull for every ad carry.

Farming is the most important thing for vayne. Concerate to your farm but check minimap for ganks. Also try to harass your enemies.
Your farm must be in the folowing levels:
10 minutes 80 farm.
20 minutes 190 farm.
30 minutes 300 farm. Now you are ok start playing with your team.
Until you reach 300 farm or full your build stay to your lane and warn your team to stay out of team fights. If they do it well you will be able to carry it .