When it comes time to clean concrete, you don’t need to be delicate; after all, it’s a very hard material.
In order to clean concrete outdoors, you can rent a pressure washer for use in combination with a biodegradable detergent. Indoors, your supplies are likely to be a bucket, detergent, and scrub brush, with or without a wet/dry vac at job’s end.
These approaches will enable you to get a long way toward removing ground-in dirt, mildew, spilled paint and most food stains. But the bad news for the fastidious homeowner is that concrete is a porous material with innumerable tiny voids that can harbor dirt, mold, and all kinds of deep, stubborn stains.
I once tried cleaning a concrete floor that had been exposed to leaky oil pans and transmissions for years and years. Power washing did very little. What helped a little, though ultimately not enough, was scrubbing the area with TSP, then hitting it with the hose. As a last resort, I used an application of muriatic acid, which successfully vanquished all of the remaining oil spots.
Muriatic acid is also useful in cleaning excess smears of dried mortar and grout, or when attempting to alleviate tough rust stains. But please be advised that you must be extremely cautious with this powerful acid. Don’t even use muriatic acid unless you really need to. If you must, then be sure to wear protective gear (including protective clothing) and always follow the manufacturer’s directions for dilution. Allow for plenty of ventilation.
My preference is to begin with the least toxic cleanser and up the ante as needed. Try applying common detergents directly to the tough spots and scrubbing with a bristle (not wire) brush. Hydrogen peroxide or ammonia also work well.
For indoor jobs, you might try scrubbing with TSP before rolling on a masonry primer and a masonry topcoat. Such a coating would hide the old stains and seal the concrete to prevent further staining.
Concrete sealer is a reliable option for avoiding stains in the first place. Choose a clear silane- or siloxane-based water-repellent sealer and apply the product with a paint sprayer or roller. Sealing will not affect the appearance or traction of the concrete surface.