What's the best way to remove dirt from a fiberglass shower floor?

http://www.doityourself.com/stry/5-tips-for-cleaning-a-fiberglass-shower-floor

The dirt is a combination of dirt and soap scum build up. Try making a paste of baking soda and water, applying it and allowing it to dry. Once it's dry, wet it with vinegar (either while or cider), let foam and scrub with a plastic scrubee.

CLR is fantastic!

Once clean and clear, spray furniture polish (good quality, not watered down) on a polish cloth, rub onto the glass surface. Do not spray directly on the glass, as you do not want the spray to get on the shower floor, it will become slippery. Apply again when you see some spots or every few days. The polish will keep the water off and you will have to scrub less. Apply to both the insides and the outside of the shower stall glass and frame. Also works great on mirrors!

Sprinkle the baking soda over the fiberglass surface of your shower, then spray with the white vinegar, causing a paste to form. Gently scrub the fiberglass tub, floors and walls with this solution using a non-abrasive sponge. Be sure to wear rubber gloves when working with vinegar to protect your hands.

I would use baking soda and water paste to scrub it. Then rinse and use vinegar to clean the baking soda paste away.