Concrete is a very porous material and will take stain color very well if you follow a few preparation steps. Anyone who has seen an oil stain on concrete knows that concrete will hold that stain practically forever. Stain removal products are available all over, but the reality is that nothing really works well. That is good news for anyone who wants to stain concrete.
Wash the concrete completely. Use a product like TSP and scrub the surface anywhere there is a discoloration. If there are stains or discolorations on the existing concrete, scrape any residue with a metal scraper then soak with a paste of TSP for a few minutes. Wash the surface again. Rinse with clear water until no residue is visible.
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There are products on the market that will paint or resurface concrete but to go cheap, use the least expensive oil base stain or paint you can find. Mix the paint/stain with paint thinner in a 50-50 solution. That is one gallon of paint to one gallon of paint thinner. Use a roller on a long pole or a string mop for a swirled effect or a broom for speckled color. Start painting.
Some areas on the surface will take the stain color differently than other areas. A design that is mottled or swirled and the irregularities of the surface will become part of the artwork. The colors should be applied wet-on-wet. That means blend and swirl and speckle all over and all at once rather than do one thing at a time. Larger areas may need more than one person to apply everything while the products are still wet. There is no way to correct a mistake. Learn to enjoy them. It's part of the art form.
Be careful about using reds. The reds fade in the sun and will become pink or orange. Blue and Green fade to a pastel color and can be difficult to apply evenly. Plan to have at least two or three colors and blend them after they are applied to the concrete. Example: off-white base color, swirled redwood stain and speckles of golden oak stain. The contrast in these colors is dramatic, but the overall effect is similar to some granites.
A top sealer should be used as soon as the surface is very dry. Interior sealers will not work outside but exterior sealers do work inside. Don't go cheap on this material. Bad sealers will yellow, bubble, flake off or be too slippery to be safe.
These techniques can be used indoors or outside. Be aware that this is a stain and almost impossible to remove. Don't get this stain on anything you don't want colored. Indoors, remove the baseboards and always use in a well-ventilated area. Oil base paint is highly flammable until it dries, so don't use it near an open flame. Follow the directions on the packages for clean-up.