The basic idea is to have creatures that can be returned from the graveyard relatively easily, while attempting to remove key threats from the board and steadily create zombie tokens.
On the reanimator front, Gravecrawler, Prized Amalgam and Relentless Dead are capable of reanimating themselves, while Lord of the Undead, Gisa and Geralf and Relentless Dead (again) help reanimate others.
On the removal front,
Bile Blight
can deal with medium creatures, especially repeated copies or tokens; while Dark Salvation may be cast for as low as 1 black mana and kill something big, depending on the board.
Compelling Deterrence
can deal with any non land permanent, which is nice; and if the opponent has no cards in hand it actually works as a destruction.
For token creation, Cryptbreaker on the early game, preferably discarding Gravecrawler or Prized Amalgam. Diregraf Colossus throughout the mid and late game. On the late game, Dark Salvation can actually create a few tokens as well, and Endless Ranks of the Dead tend to fill the board in a few turns, even if cast relatively early
On the sideboard:
Negate, especially to deal with board wipes other than Supreme Veredict.
Any problematic spell that can't be removed or countered may be extracted with
Stain the Mind
, which can be played by turn 3 with convoke if on curve.
Tormod's Crypt to deal with graveyard decks. I use this instead of Relic of Progenitus since removing my graveyard is undesirable
Phyrexian Crusader against white and red removal heavy decks
Finally,
Bile Blight
in case more removal is needed
