Most good tile setters will tell you that a high-quality tile project always starts with subsurface preparation. A tile shower floor uses a mortar and sand mixture as a subfloor. The tile setter dry packs the mortar mixture in the shower pan. He then cuts in the floor's slope with a straightedge. Once dry, the mortar gives the tile a solid surface to rest on. An improperly created subsurface causes high and low spots in the finished floor. Sometimes it takes as long to prepare the subsurface as it does to lay the tile.
Remove the shower drain cover and set it aside. Stuff a rag into the top of the drain hole. The rag prevents debris from falling down into the drain pipe. Hold one end of a bubble level on the drain opening and slide the other end of the level across the existing tile's surface. Check the floor's slope. When measured from the drain opening to the furthest wall, the level should show about 1/4-inch of slope per foot. Slide the level across the floor and mark all high and low areas with a wax pencil or permanent marker.
Put on all safety equipment, including safety glasses and leather work gloves. Remove any raised tile, using a hammer and chisel to dislodge the tile. Do not worry about damaging the neighboring floor tile. A single raised tile can hold enough water to create a puddle. Remove all of the old caulking material from the perimeter of the shower floor, including the caulking covering the bottom six inches of each of the wall's corners. Thoroughly clean the entire shower stall, using any household cleaner that removes soap scum and hard-water deposits.
Mix a white-colored thinset in a bucket, using the thinset manufacturer's instructions. White-colored thinset will not bleed through the new shower tile's grout. Dampen the floor with water. Fill any dips or missing tile in the existing tile floor with the thinset, using a flat trowel to feather the thinset into the surrounding tile. If the existing shower floor does not have the proper slope, build up the low area with thinset. Run a straightedge across the floor's surface and shave off any high areas of thinset. Let the thinset dry before continuing. Double-check the floor for slope and dips with the level. Continue to add thinset to the problem areas, as needed. If the added thinset created a high spot, rub the high spot with a sanding stone or cinder block. Clean up all of the debris.