Vayne is a champion who has a decent early game when you know how to play it right, but is really supposed to be more of a late-game hypercarry. She's kinda like Twitch, another late-game hypercarry who, if played well, can be an extremely oppressive lane bully. The thing that makes Vayne so difficult, though, is her short range. 500 basic attack range, as compared to most champion's 550. Who were you playing? I saw someone down there mention Lulu. Level one she goes to trade with you, you don't just take it; you hit her ass back and throw your Glitterlance at her.
Looking at the stuff from replay.gg over there, here's your first problem: you built full AP as a support. Start
and 3 HP potions. Build into
and
first back, if you can. If you can't, just pick up the Frostfang and the Ruby Crystal. That's 900g, easily achievable by first back if you started Spellthief's. Next back, pick up your Frost Queen's Claim, and from there go into building some AP utility items.
,
,
, and
are all good choices. You can also build more tanky if you need defense. I'm an ADC main, and if you built
as my support Lulu, I would be very upset with you.
Your second problem is your runes. I have no clue wtf that rune page is, but it should be 9x hybrid pen reds, 9x flat armor yellows, 9x flat mr blues, and 3x AP quints. Hybrid penetration is because you'll be autoattacking a lot in lane fights, and for Lulu especially hybrid pens give you more overall damage than just AP or mpen.
Those are your biggest problems. Masteries look fine, though depending on the lane you might want to take Windspeaker's instead of Thunderlord's.