To repair a brick chimney, first clean the interior and exterior as thoroughly as possible to locate spots that need repairs. Inspect the lining to see if it needs to be replaced; if the lining is loose, it's often best to remove it and install a new one.
Use a chisel to inspect each brick, and remove any that are loose. You can reuse bricks that are still in good shape, but dispose of those that have damaged edges or cracks. Use a paintbrush or similar device to wipe away as much debris as possible to ensure that replaced bricks stay in place.
Use a sponge to wet the repair spots repeatedly, but don't drench the area. Repeat this process until the surface stays damp for at least 10 minutes. Remove any mortar that isn't firmly attached to the chimney. You should also moisten the replacement bricks.
In a plastic bucket, mix the mortar according to the instructions, and use a trowel to apply it to the chimney. If the mix drips when you lift it, it's too wet, so add more mortal powder to the bucket. Apply the mortar to the chimney and slowly press the brick into place, using the trowel to wipe away excess mortar. Make sure you give the mortar plenty of time to dry; two to three days is typically sufficient.