I'd say Vayne is a terrible choice for a new ADC. She's way too difficult for someone who doesn't understand the role.
Learn how to kite (I'm sure there are YouTube tutorials to help)
Learn how to abuse the brush in bot fights. If the bushes aren't warded you can dip in and out of them so the enemy ADC can't target you for autos
Learn what ADCs go with what Supports and what supports will ruin you.
Taric + Draven is a pretty great combo, but Morgana + Draven is way better if the enemy support is a Thresh/Blitzcrank.
(Spell shield the Hook)
Counter picking isn't super relevant bot lane. As long as your support is efficient with your ADC, it's basically a skill matchup (unless you're actually hard countered on rare occasion - like Vayne is hard countered by Draven)
As a final note, is recommend you drop Vayne for an easier ADC. MF, Jinx and Ashe are decent starting points.
If you're really set on playing Vayne, have a friend play Blitzcrank. Amazing combo :p