Use a general purpose graffiti remover spray as soon as possible after noticing the graffiti. Choose one with low odor, suitable for the type of surface vandalized, such as brick, stone, metal or concrete and the type of mark left, such as paint, marker pen or ballpoint pen. Spray on and leave for a few minutes. Rinse with water using a bucket and sponge or spray.
Use turpentine or mineral spirits alternatively or after trying the general purpose graffiti remover. Put a little on a clean, low nap rag and daub it against the graffiti, using a clean part of the cloth each time to absorb and wipe away the softened paint or other substance.
Try naphtha, isopropyl alcohol, acetone or methylene chloride for more stubborn graffiti stains. Note naphtha is effective for removing crayon marks. Be aware isopropyl alcohol is effective for tackling graffiti drawn with magic marker. Take special care with acetone and methylene chloride as they will melt some plastics.
Take the advice of Minneapolis Police Department and repaint the whole area where you find widespread graffiti as this may be easier, cheaper and safer than removing the graffiti. Use stain blocker first to ensure the marks don't come through the paint. Choose an oil-based paint as close as possible to the tone of the original color of the vandalized surface to return the surface to virtually how it was before the attack.