First of all you'll need a timer. First you need to measure the time in between activation of vampire mode and when it ends. (Mind that this includes the cast time and not just the duration of vampire mode, so if the duration is 30 seconds, the time in between activation and end of vampire mode will be 32-33 seconds).

Now to get the zombie:
1) Transfrom into a vampire and start the timer.
2) Go kill any random monster you can find and wait till your vampire form has almost ended (mind that corpses dissapear after 20 seconds so make sure there's less than 20 seconds in between you killing the monster and the transformation to non-vampire form)
3) This is the important part. Get your "awaken dead" skill ready and cast it on the corpse 1 second before your vampire form ends.
4) congratulations :) You should now have a zombie while out of vampire mode.

This might be the hardest part. In order to get new zombies your zombie will have to make a kill.
It wil not work if you kill monsters with your character. Every time a zombie kills a monster there is a 50% chance that the monster will turn into a zombie.

The easiest way to do this is get a monster to very low health yourself and then let your zombie finish him off. Try to intercept as many incoming damage from the monsters so your zombies don't get killed in an early stage of your army. If al goes well your army will start growing and after a while your army will be able to recruit new monsters without your help.

Things that will destroy your army:

• Death of your character
  
• Transforming in a vampire again. (When the vampire mode ends again your army will vanish)

Other stuff that might be interesting:

• If a quest requires you to kill a certain mob you will have to kill the mob yourself because the game will not consider the mob to be dead if you turned it into a zombie. Monsters will however still drop loot when they get converted to zombie, just like when they die.
  
• Zombies act like regular companions so they will teleport to you if they get out of your field of view.
  
• Zombies are weaker than their non-zombie form so watch out with letting them attack big groups.
  
• Every type of mob can be converted (even dragons)