Cut through the existing carpet with a utility knife to reveal the plywood subfloor below. To prepare the subfloor for underlayment, pull up the carpet pad and pry up all the tack strips. It's important to start with a smooth surface, so pull out any remaining staples and vacuum all the debris.
With the sub-floor in good shape, begin setting the underlayment. Underlayment, or backer board, provides a good foundation for the tile. Without it, tiles can crack as the house settles and shifts over time. In order to fit the backer board into each nook and cranny, cut the 4' x 4' boards down to size using a utility knife.
For tough cuts around the sink or sewer opening, transfer a group of measurements to low tack tape on the tile. Using tape gives an exact line to follow, so there's less room for error.
If the grout joints are 1/8" or larger, use a sanded grout for strength. As the house settles and shifts, the grout acts as another buffer so the tiles don't crack over time. Clean the tile surface, and use a rubber grout float to pack the grout in all the joints (Image 1). Once you fill all the joints, use a wet sponge to clean off the excess grout (Image 2). Wipe the joint while using a 45-degree angle to not remove the grout from between the tiles.