Cover your counter and put on a mask and safety goggles. Cover your counter with plastic sheeting to protect it and make cleaning up easier. Put on a pair of safety goggles to protect your eyes against dust. Finally, put on a mask suitable for working with fine particles. Most dust masks and respirator masks come with a description of what they are used for, such as sanding dust, aerosol, etc. Choose the one for dust.
Make the tile where you wish to cut it. A pencil may work just fine on a slate or ceramic tile, but if the tile is glazed, you should switch to a marker. Try to be as precise as possible for this step. Installing a new electrical fixture will require you to get inside the wall. Mounting a towel rack does not.
Cut along the top, bottom, and side edges. If you need to get inside the wall, then you should cut through the dry wall as well. A dremel rotary cutter with a diamond tile blade will work for most tiles. If your blade can’t go around the corners, skip them for now.
Use an oscillating cutter to cut through tight corners. While a dremel rotary tool will work for most lines, it won’t work on tight corners. For that, you should switch to an oscillating cutter instead. You may have to experiment before you find the right one for your type of tile. A multi-surface blade seems to work better than a tile blade, however.
Pull the tile away. Wedge a thin knife or spatula behind the tile and pop it out. If you had to cut through the wall, try not to lose anything inside the wall. Your hole is now complete and ready to finish.