Run a paint brush over the cracked area to remove any loose dust or debris. Also get the brush inside the crack as much as you can to clear out debris that could interfere with the repair.
Wash the brick with warm water and several drops of dish soap to further eliminate dirt. The cleaner the brick is, the better the repair bonds to it. Rub the brick with a scrubbing sponge, rinse with regular water and then allow the brick to dry.
Insert a concrete bonding material or mortar into the crack using a trowel or a putty knife. Fill the crack as much as possible and then wipe away any excess with a rag before it hardens.
Sand down the repair with fine sandpaper once it has fully dried to smooth it down evenly with the rest of the brick.