Knock out all the pieces of broken brick with a sledgehammer and chisel. Make the crack bigger in the brick wall with the chisel. Then clean all debris out of it with a wire brush.
Mix sand and mortar with some water in a mixing bucket. Place the mortar on a piece of cardboard.
Add mortar coloring to the freshly mixed mortar so it matches the old mortar. You can also see if the new mortar will match the old mortar by letting a piece of it dry. When it drys you will see the true color of the new mortar.
Use the circular saw with the masonry blade to cut the replacement brick to fit the hole.
Wet the cut brick and apply mortar to the sides of the brick. Put the newly cut replacement brick in the crack where the broken brick used to be. Then use a sharp trowel to solidly pack the rest of the crack with mortar.
Finish the outer part of the brick by matching the joints together. Use a trowel and jointer to fix up the joints near the surface of the newly grouted brick. The surface of the brick needs to match the other bricks on the wall as closely as possible.
Cure the crack for one week. During the week you will need to spray the brick with water a few times a day. After one week it will be completely cured.