Lift the tile directly above the broken tile slightly. Wedge a wood strip gently underneath the raised tile to hold it in position.
Put on safety goggles. Tap the intact portion of the broken tile gently with a hammer to break it into shards. Remove the broken pieces.
Pry the tile's old nail out of the roof with a pry bar, taking care not to inadvertently damage the surrounding tiles.
Drive a tile clip into the roof with the hammer. Position it so the hooked portion at the bottom of the clip is aligned to hold the replacement tile in place.
Slide the new tile underneath the tile supported by the wood strip until the bottom of the new tile rests securely within the tile clip.
Remove the wood strip and lower the old tile above the new one onto the new tile.