Laying tile of any sort is a complicated process of fitting the tile just right so that the least number of partial tiles are used. Whole tiles are faster to install and look better to the viewer than partials. Unfortunately, any tiled surface is likely to require a few partials, so cutting the full tiles to fit will be necessary. A quick all-around cutting tool for tiles likely to be used by many DIYer tile installers is the table saw. There are few tiles that a table saw won't cut through, but to do so cleanly without breakage or chipping requires that you approach the cutting process prepared beforehand and knowledgeable about cutting procedure.
Measure the space needing the partial tile and transfer that measurement to the rear of the tile, marking a cutline along the tile back with a piece of chalk or grease pencil. Use a straightedge to help you to mark a clear, even cutting line.
Place the tile onto the cutting platform of the table saw with the cutting line aligned with the saw blade. Make sure you've attached a blade that's appropriate to cutting the tile material. For example, if cutting a ceramic tile, you should use a diamond-edged blade, whereas for slate tiles a masonry blade is more appropriate. Consult the tile manufacturer for blade suggestions.
Put on a pair of safety goggles to protect your eyes from flying particles, a face mask to protect your lungs, and work gloves for hand protection.
Turn on the table saw and slowly push the tile against the blade, allowing the blade to apply the force necessary for the actual cutting. Cut through the tile in a single continuous motion; turn off the saw once you've completed the cut. Remove the tile from the platform, wipe the cutting edge with a rag and then place it into position on your tiling surface.