To make a zombie, you first need a dead sim. And a sim that knew the dead.
There are two ways to do it:
One: REQUIRES UNI. Get the Resurrect-o-Nimitron from the career catalog (From the Paranormal career)
Two: Dial up Grimmy. Pay about $1000 in simoleans and they should be a zombie.
OR:
One: REQUIRES FT. Get the Genie lamp, wish to resurrect.
Two: There's a small, random chance that the sim will be zombified.