Cut your tiles with a wet saw to fit them around the shower drain. Lay them in position around the shower drain, leaving a gap of 1/4-inch between the drain and the tiles.
Place two or three spacers in between the shower drain and the edges of the tiles to prevent them from moving closer to the drain.
Mix the grout according to the manufacturer's directions. Allow the grout to sit for 10 minutes to ensure there are no bits of dry grout powder in the mix.
Scoop grout onto the shower tile floor using a margin trowel. Spread it over the tile with a grout float, ensuring that you push grout into the 1/4-inch gap along the edge of the shower drain.
Hold the grout float at an almost perpendicular angle to the tile. Use the long edge of the float to scrape off and remove excess grout on the tile and around the shower drain.
Fill a bucket with warm water. Soak a clean sponge in the water and wring out the excess water.
Wipe the tiles and shower drain in a circular motion to remove excess grout. Rinse your sponge frequently and continue wiping. Allow the grout to set around the drain and tile for 48 hours before you use your shower.