Wait until your fireplace is completely cool. Remove everything that's in front of your fireplace, such as a screen and fireplace tools, as well as everything inside the fireplace.
Sweep the fireplace floor clear of debris and any loose mortar.
Place the tip of a brick chisel on the mortar between the broken brick and the adjacent brick. Tap the back of the chisel firmly but gently with a hammer to break up the mortar. Work your way around all sides of the brick until your are able to pry it up from the floor of the fireplace. Repeat the process for any other bricks that need to be removed.
Use the chisel and hammer to clear away the old mortar from the spaces where the broken bricks were.
Mix a small amount of mortar for the new brick or bricks. Follow the instructions for whatever mortar you are using -- this is usually two parts sand to one part mortar and enough water to make a slurry.
Use a trowel to apply mortar to all four sides of a new fireplace brick, then place it in the space where the old brick was. Scrape off any excess mortar from the sides and top of the new brick, using the trowel. Use a damp, disposable rag to wipe away mortar from the top of the brick.
Smooth out the mortar in the joints with a thumb joiner.