Clean the existing surface. Use a mild detergent and a sturdy scrub brush to remove any visible debris or particles, as well as invisible grease and soap residue. Rinse well and allow the fiberglass surface to dry completely.
Measure and cut a piece of concrete backerboard to fit the area over your fiberglass floor. This type of backerboard has fiberglass on both sides that helps create a waterproof backing for your tiles. Depending on the size of your floor, you may need to use more than one piece. Use a circular saw with a carbide blade to cut the backerboard.
Apply a coat of thinset mortar over the top of the clean fiberglass surface, using a notched trowel. Lay the backerboard over the thinset, pressing it firmly into place. Lay out the backerboard by butting the pieces as close together as possible. Nail the backerboard into the underlying joists to help hold it firmly in place. Tape the seams between the backerboard joints. Apply backerboard joint compound over the taped seams, smoothing it evenly with a straight-edged trowel. Let the joint compound dry completely.
Create a layout line for your tiles by dividing the floor into 4-foot sections. Use a chalk line to snap guidelines over the center of the surface. Tile one section at a time.
Apply tile mortar to one section of the backerboard, using your notched trowel. Set the first tile in a corner of the section, using tile spacers to hold it an even distance from both of the outside edges. Use the size of tile spacers recommended by the tile manufacturer. Spacer size varies according to tile size. Wiggle the tile to seat it firmly in the mortar. Place tile spacers on the open sides of the tiles and set two more tiles in place. Complete each 4-foot section in this manner. Allow the mortar to dry completely.
Remove the tile spacers. Apply the sanded tile grout to the joints between the tiles using a grout float. Press the grout into the gaps. Wipe the surface of the tiles with a damp sponge to remove excess grout. Let the grout dry. Remove any remaining cloudiness from the surface of the grouted tiles with mild detergent and warm water.