Basically, get used to his auto attack animation.
As far as farming under tower, if you tap E on the wave, turrets will hit casters once, allowing you an easy last hit with an auto. Melees get 2 hits from the tower after you e tap and you can last hit them with autos.
If you don't use E to lower their hp by that little amount, you have to auto immediately when the turret targets them, then auto them again after.
This is why you take E lvl 2 if you're getting pushed in, and W lvl 2 if you're pushing out to avoid all-ins or ganks.
I run full HP, CDR, and AP/level on him. The AP allows you to go pretty much any item you need and still have fantastic sustain+damage. Using AD runes will just gimp you in the long run. If you REALLY need help, take the last hitting mastery in the utility tree.
Remember that you can tap E if you see you're gunna miss a last hit with a basic attack.
Start boots+4 pots; helps you avoid engages, avoid skillshots, CS, and get into trading stance more reliably.
Finally, as Vlad, your goal is not to harass. You do if its convenient, but CS is much more important. If I see they don't heavily avoid CR procs, I'll try to get them with it, but otherwise I afk farm and only Q them if they go into range of it.
Focus on farm, no matter how much of a lead or health advantage you have. Getting yourself ahead is more important as Vlad than putting your opponent behind because you WILL outscale them. You want to make that happen as soon as possible. Don't be aggressive if it costs you CS. Only go for it if its essentially free.
**Vlad is not about winning lane, Vlad is about not losing lane. **