Protect the immediate area from dust and damage by covering counters, appliances and the floor with a drop cloth.
Wear a dust mask and safety goggles, because removing brick veneer creates a lot of dust and it's possible for pieces of mortar and brick veneer to fly off at high velocity.
Place the chisel on the mortar of the top left corner brick. Tap gently with the hammer at first, then increase the force as you get a feel for what it takes to crack the mortar. Tap all the way around the brick.
Insert the flat end of the crowbar into a crack in the mortar. Press firmly down until the brick releases from the mortar. Move the crowbar around as needed to pry the brick out. Toss the brick and any large mortar chunks directly into the garbage can for easy disposal.
Repeat with the next brick and work your way across, going from top row to bottom row.