Always look to harass Vladimir when his Q is on his cooldown (9 seconds at level 1) especially when he doesn’t have his empowered Q.
Vladimir's W has a 28 second cooldown at level 1, find a way to bait out the W (whether that be through a gank or a very threatening all in) and then look to secure the kill since he doesn’t have an escape.
Vladimir is very immobile, but is a great pusher, buy Control Wards to deny vision so that he is easier to gank. Play around his empowered Q so that you can set up the most optimal gank without him healing.
Vladimir's teamfighting power comes from his large amount of AOE and his R. Try to stay distanced from each other so his Ult doesn't amplify and damage several targets.
Vladimir's healing is his strongest quality as a champion. His empowered Q and the second half of his R can keep him in a fight for much longer than expected. Build Grievous Wounds items (Morellonomicon or Mortal Reminder) to keep him from healing as much.
Even in the late game, Vladimir's mobility is very limited to Protobelt and his W. Look to lock him down to prevent him from escaping and using his Q since he is going to be easier to hit with skillshots than other champs.
At level 9, Vladimir's Q is on a 5 second cooldown without cooldown reduction or Cosmic Insight. Look for brief skirmishes or trades when it's on cooldown.
2. Zhonya's Hourglass is a core item for Vladimir that provides him with a range of benefits. Try to to bait out his W and his Zhonya’s before looking to finish off Vlad. If he pulls of the stasis, back away to deny him a free empowered heal from his Q.
When Vladimir doesn't have his R up, he is very weak and cannot trade back as effectively in all ins. Send 2 or 3 people to deal with a lonely Vladimir so that he is removed from any upcoming teamfights.