Note : In depth guide will only talk about the first build, just replace with the right item.
I will just separate Vayne Solo Lane and Vayne Duo Lane in this part, lane tips can be apply mid game too.
Vayne Duo Lane
First, check who you are laning against, look at the AD carry AND the support to determine with which item start.
If you are blue cover your jungler until 1:20 minute mark or longer if you invade the enemy jungle.
If you are purple help your jungler with his blue if he begins with it.
Go with your support to your lane. Until level 4, I suggest you just to farm and last hit as much as you can : remember if you last hit under tower, wait 2 hits of the tower on melee creep + autoattack and 1 tower hit + tumble on caster creep, harass your opponent if he does but DONT spam tumble and DONT SPAM your E, mana cost of the E is huge early game. When you hit 4, harass your opponent with your autoattack, and try to proc your W a lot. If a trade goes wrong just E the enemy carry even if he cost you a lot of mana.
To maximize your damage try to autoattack the enemy AD twice and tumble to proc your W, which will deal more true damage. As I said don't spam your E and I think you must not use it before level 5 to deal more damage. See if the enemy AD is near a wall (keep last hitting in the same time). If not look at the support which is often in the brush. If he's squishy like Janna, Soraka, Sona ask for a ward and pin the support to a wall, try to tumble to proc W, but if you have to tumble to position yourself to use your E, do it. Try to be aggressive with Vayne early game, don't worry if you don't kill someone in the laning phase, you are a carry AD, your damage will increase throughout the game especially with Vayne.
If you are ganked knockback the jungler or the enemy AD carry, use flash and cleanse if necessary.
For your first back you should have at least 1400 gold or more. (of course if you are low hp without 1600g and without healer, just back and get :
Of course if you back with more than 1400g (in SoloQ) just get
You should have ~~ 80 CS at 11min.
Buy wards even as AD carry buy wards if you can, buy some pots too.
Dont forget, you are bottom lane, the drake must be warded and must be protected. If you die the enemy will probably try to do it.
That's why play safe early game, farm and harass when you can. If your jungler gank listen to him, if he's in the enemy jungle and in difficulty, help him even if you miss some last hit.
Check your CS often and try to be in teamfight for the drake. 175 CS at least at 20min.
Solo Lane Vayne
Some differences, you max your W, proc it as much as you can, it will hurt A LOT the enemy laner. If he uses skillshot dodge them with tumble. Farm and try to deny your opponent, true damage can take down the enemy laner quite easy even an offtank. Ward around you, you are an easy prey for the enemy jungler. Dont overextend. Farm, deny and play safe. You are solo if you fail without getting ganked it's your own fault.