Ok, Vayne is SO squeashy, she has to rely in positioning and escaping even more than the AVG ADC.
Now, what has worked for me:
Farm hard early, but you have to KNOW your matchups. Caitlyn will poke you hard, while Sivir for example, is easier to combo her a bit and retreat.
A good combo with Vayne is at lvl 3: autoattack, tumble + autoattack, condemn.
At lvl 3, condemn will trigger silver bolts and do some desdcent dmg. As SOON as your condemn hits, pull back to avoid retaliation from support or minion aggro.
IF you see them close to a wall, CONDEMN them. You've to teach them respect, and this will help you farm faster.
If you stun them, tumble for a second hit AND if the support doesn't come, hit fast for a third auto and BACK OFF again.
Those tactics do descent damage and if you are lucky, you'll get them burn their Flash or heal, so you'd have an advantage.
Learn the mechanics for Tumble and practice moving fast the mouse to the tumble direction to actually tumble there. Remember Vayne tumbles to where the mouse is pointed (Like flash) and not to where you're watching, you've no idea how many times I died when learning her because I'd tumble directly towards the enemy or to a skillshot (Once I tumbled to a Nidalee Spear, LOL).
Contrary to some belief, you should NOT start with attack speed, so the order in which I build is:
BotRK -> boots -> AS boots ->From here I get like 1.35 attack speed, so I can decide if I go IE or Phantom Dancer (USually Dancer first) Then IE.
After IE i build either LW or BT, depending on the enemy tankiness.
Last item, your favorite deffensive item.
So, in lane: Farm and engage hard after BorK or LVL 6, those are BIG power spikes.
in teamfights, stay behind the tanks, Vayne has low range, but her condemn/tumble give her a lot of utility. If an enemy flanks, and he gets near a wall, CONDEMN
Now, some "(Not so)hidden" Vayne tricks:
Making an enemy hit broken turrets/structures with condemn, will stun them.
Tumble will tumble through some terrain (Like Anivia's/JIV wall). At least it used to, idk if they changed it, so try it.
Condemn is as a displacement, so in a duel, u can use it to cancel channels.
You do NOT get vision if you condemn someone into grass.
The invisibility from tumble while ulting will make certain skills stop aiming you (Like Fiora's ult)
Maybe there are some extra tips to share, but that's all i can think of right now.
Practice, practice practice.
Learn who counters you.