Undead share many traits with golems, and the magic used to animate them is similar. However, the physical structure of an undead is already there, and designed to move in a way the creator is familiar with. Depending on the state of the brain, there are already some good existing patterns to reuse. The creator combines these resources with a framework and set of commands stored in an ethereal cloud known as a ghost.
A ghost embedded back into a physical body produces a decay-inhibiting system. The undead do need to eat, but if they go too long without food they merely fall into torpor wherein they wait for food to wander by. In torpor they've only vague visions and scents to alert them to passing prey, and if they remain in this state too long they risk being locked in, released from their own whispers only after years or decades have slowly drained the last wisps of vitality from their shells.
Incorporeal undead are ghosts given greater volumes of ether and activated.