Clean the surface carefully to remove all traces of grease, dirt, moisture or other substances.
Decide what method you will use to remove the paint: scraping or by applying a solvent or stripping agent. Scraping or sandpaper can mar the concrete surface. Solvents and stripping agents can be toxic and don't work for all types of paint and concrete surfaces.
Remove the paint using the method you've selected.
Collect stripped paint for disposal. Contact your local hazardous materials coordinator for disposal information.
Rinse the concrete surface with water.