Purchase water-based urethane coatings only. Do not use epoxy because it doesn't last as long as urethane.
Integrate the floor cleaning and screening processes. Tack the entire floor by submerging a towel in cleaning solution, squeezing out excess water, securing it to a large broom and pushing it across the whole area. The floor should appear damp but not puddled after being cleaned in this manner. Do not use mops. Replace towels as they become very dirty.
Attach a sanding screen to the floor buffer. Do not use soaps, detergents or even water during this phase to prevent unwanted gloss. Peform the buffing in methodical fashion from end to end, pushing the floor buffer in a straight line. When you're done, you can sweep the floor with dampened towels to remove any leftover particles or dust.
Coat the gym floor. Consult the manufacturer's guidlelines on coating thickness. Use the recommended applicator to apply the finish. Allow to coating to completely dry before allowing anyone onto the floor.
Sweep or dust mop the floor daily to help maintain its shine. Perform a wet towel cleaning at least once monthly.