Attach a masonry bit to an electric drill. Set the depth of the drill to the depth of the bricks in the porch. Drill holes into the mortar surrounding the broken bricks to aid in mortar removal. Place the holes on all sides of the brick with about 1/4 inch of space between each hole.
Place a chisel tip across adjacent mortar holes. Use a hammer to hit the chisel with a light amount of force several times to cut through the mortar. Chisel through the mortar surrounding the brick on all sides, beginning along the top of the brick, then the sides and the bottom.
Remove the broken mortar from the joints using the chisel, then pull the brick away from the porch. If the brick does not pull away easily, slide a prybar into the joint between the broken brick and the brick next to it. Apply pressure to pop the broken brick from the space in the porch. Remove any mortar still in the space with the chisel and a wire brush.
Use a spray bottle filled with water to wet the emptied brick recess. The water will keep the whole bricks in the porch from leeching moisture from the mortar used to place the new brick.
Butter the edges of the replacement brick with a 1-inch-thick layer of thinset mortar using a trowel. Place the brick into the recess, pressing it into place until level with the surrounding bricks. Remove any mortar that squeezes out of the recess with the trowel.
Place a carpenter's level across the new brick and adjust the position of the brick witin the recess to level it out. Allow the mortar surrounding the brick 72 hours to cure before walking over the porch and 10 days of curing before heavy use of the porch.