A tile cutter (Image 1) cuts through tile in two steps: First, its round blade is pushed across the tile to score a line where the tile is to be cut (Image 2). Then the foot to the back of the blade is clamped down onto the tile to cut through the scored line (Image 3).
A coping saw with a rod blade can be used to cut through softer tile, such as Mexican tile. Because the coping saw cuts in small strokes, it's especially handy for cutting irregular shapes.
To drill through tile, use a carbide-tipped bit or a masonry bit. To protect the tile when drilling, place a tiny ball of plumbers' putty on the spot where you want to drill. Use an eyedropper to apply a small drop of water to the center of the putty ball. The wet putty acts as a shield for the rest of the tile as you drill the hole.