Who would be a good support for her?

Any support with a good amount of peel; Janna, Annie, Thresh, and even Braum given the lane opponents.

What is positioning/How do I know where to be?

Ideally, as with any adc, you want to hang back and have your support peel whoever tries to dive you. Once they're dead move onto the next target. Your short range limits your team fighting prowess, but your clean up ability afterwards is really strong.

What should I be focusing on in lane?

This is contingent on circumstance and who is in lane with you. I guess in the most general sense, it's better to focus the enemy adc.

What should I be focusing on late-game?

Assuming it's a 5v5? Whoever dives you, simply put. Once they're dead move onto the next target.

I've been told to build BOTRK > Beserkers Greaves > Phantom Dancer > Infinity Edge > Last Whisper > Bloodthirster. Is this a good build?

Simply put, yes. BT is interchangeable depending on how the game is going.

When should I use each of my skills?

Uh, well, again this is contingent on circumstance. Q is a great tool for positioning and kiting, and your E is great for dueling and self peel. Always remember that your E will procs the third silver bolt passive on your W.

Should I be applying pressure, and if so, how do I do it?

In most cases you will not be the aggressor in lane, at least not until you get BotRK. Once you have BotRK and your ult, your dueling potential is through the roof (assuming you aren't way behind).

What are some combos I'll be using? - How do I make good trades?

I'm not a Vayne player, so I can't really cite any secret tips or tricks. But I can say that utilizing your E is going to make or break you as a Vayne player. Always consider your environment an ally, and position yourself to best take advantage of it.

What summoner spells should I be taking?

Flash/Heal, there's really never a time when these two aren't optimal.