Buy Grievous wounds, shit on him in lane, because he's going to outscale you starting around level 10, no matter who you are, so long as he didn't feed. At 3 items he can start to 100-0 people with EQ.
While in lane, go in for trades while his Q (in particular) but also his E are down, since they have obscenely long CDs early on (9s at level 1 on his Q, 13s at level 1 on his E). If you have to choose between his E being down and his Q, pick his Q, because Vlad will always max Q first, since his E does most of its damage through scaling and has a health cost that makes it not good to spam early. Out of lane, and post level 9, this is pointless because he'll more or less always have his Q and E up, as with 40% CDR (CDR is Vlad's best non-AP stat), he has a 3s CD on both his Q and E when maxed.
Don't stand near him when he has his empowered Q up, because he will basically always out trade you if he can get it off, because it gives him a very large heal (+% missing health, scaling with AP) and has the highest base damage of any ability in the game.
Starting Doran's Shield helps, because the highest winrate Vlad build takes Deathfire Touch, and Doran's Shield is strong against it.
Also, if it's up, don't let Vlad get Cloud Drake, which compensates for his lacking out of combat mobility and lowers his map presence overall.
When fighting Vlad, if you have any CC at all, save it for while he's charging his E. Don't let him get a fully charged E off on you, especially late game, because you'll get chunked for ~1200 damage. Think of Vlad's E as an AoE Syndra ult-lite.