First, clean the area with soap and water. Then, use a chemical stripper. You can find these at any home improvement store. You can use sandpaper to remove the rest.
To remove water based paint from concrete is very simple. The easy way is to use a pressure cleaner. If you do not own one they can usually be rented at any local hardware store. The pressure cleaner will literally make the paint come right off the concrete with very little effort.
One of the best products to use is PEEL AWAY 7 by Dumond Chemicals. You can find it at most paint stores or hardware stores. It is environmentally safe. It can be used on all interior and exterior surfaces.
Soak up wet paint. Start scrubbing, bucket , soap, water and scrubbrush. Powerwasher is ideal in this situation. DRIED PAINT:Apply paint strip and scrape. wash with soapy water.