A clean mattress makes a bigger difference than you'd think. Here's the most effective method, plus the mistakes most people make.
Remove all bedding. Vacuum the entire mattress surface, sides, and seams using the upholstery attachment to remove dust mites and dead skin.
Sprinkle a generous layer of baking soda over the entire mattress. Let it sit for at least 30 minutes -- ideally several hours. Open windows for ventilation.
Mix 2 tablespoons hydrogen peroxide, 1 tablespoon dish soap, and 1 tablespoon baking soda. Spray on stains and let it sit for 10 minutes.
Blot treated stains with a clean cloth. Once dry, vacuum up all baking soda residue from the entire surface.
Rotate the mattress 180 degrees (or flip if double-sided) to distribute wear evenly. This extends the mattress life.