Slip on a pair of sturdy work gloves and safety goggles, then remove any nails holding down the broken or cracked tile with a crowbar or hammer.
Lift the tile found above and to the right of the broken tile. To remove a broken tile, slide a piece of wood or the flat end of a crowbar under the tile to slightly lift it off the roof. Repeat this process on the tile found under and to the left of the broken tile as well.
Break the broken tile apart with a hammer. Perform this action carefully to prevent damaging the adjacent viable tiles. Remove broken tiles with your gloved hands and place the shards into a plastic garbage bag.
Slip the new tile into place, ensuring that it securely fits beneath the two tiles held up by the pry bar or wood. Carefully remove the pry bars or wood chunks from beneath the tiles, starting with the lower left one. The tile is now steadily in place.