Dry the floor. Turn water to your shower off and run a dehumidifier until all dampness is gone from the surface. This may take several hours to a day or two. Close all windows and seal the room from outside humidity.
Scrape away any old paint and remove dust and debris from the floor. Sweep thoroughly and use a strong vacuum to remove fine dust that may be caught in small cracks and pockets. If you can't remove all of the loose dust and paint, use a water/baking soda paste to scrub the surface. Make sure the floor is smooth. Paint must be able to stick directly to the concrete. The slightest amount of debris can cause problems.
Apply muriatic acid to prepare for the painting. With a spray bottle, get your floor damp with a light coat of water. Pour a gallon of water into a 5-gallon bucket. Add 1 1/2 cups of muriatic acid to create a 10-to-1 water to acid ratio. Use a scrub brush to scrub the floor thoroughly with the acid solution. Allow to dry for 24 hours. When your floor is dry, it should feel like sandpaper.
Paint your shower floor using heavy duty, outdoor epoxy paint commonly used on garage and shed floors. Roll the paint evenly as directed by the paint manufacturer. If the first coat of paint does not thoroughly fill in pockets or cover the floor wall/floor seam, apply a second coat. If you want your floor to have more texture to reduce slipping when showering, add a handful of sand to your paint. Allow the surface to cure for 24 hours before walking on it or running your shower.