Easiest, fastest, and most precise way to cut Ceramic Tile
You need a diamond tile saw, where you put the tile on a platform and slide it past the water-cooled blade. They are fast, precise and good for the hardest porcelain tiles. Expect to pay $300 and up. Straight cuts are the easiest. To cut out a square corner, make the two cuts with the tile upside down. The back of the tile will be a mess, but the business-side will be tidy.

If you want the cut edges to be velvety smooth to walk on or rub skin against, use some damp 400 grit wet/dry held at a 45degree angle to the sharp edge.

Score-and-snap tools are fast for cut edges that will be hidden by a baseboard.

Cheaper saws where you push the tile through (like a table saw) are OK, but not as fast and versatile as the sliding-table models.

For round holes for shower heads etc, use a diamond hole saw. If the tile is porcelain, submerge it in water on a bit of plywood while making the cut.

For rectangular holes for electrical boxes, use a diamond hole saw for the four corners, then use the tile saw from the back, like a mitre saw. 

The wet diamond blade is pretty amazing - it will cut through tiles but is fairly safe on fingers. You can hand-hold tiles for tricky trimming without too much danger. (at least so far!)