Research your house's history, with an eye toward learning what colors the builders used when it was first built. Quite often, American Foursquare homes were first painted in dark, rich colors, including dark green, Indian red, and brown.
If your American Foursquare house is built of wood, choose at least two complementary colors of paint based on your research -- one for the trim, and one for the walls. Scrape and sand old paint, but don't remove it completely; this will help to ensure that the new paint adheres properly. Inspect the wood, and repair any damage before you paint.
Often, American Foursquare homes made of brick or other masonry were painted when first built. Inspect the building and check your records to determine what color, if any, the original builders used. Repaint the brick before painting, replacing old mortar to ensure leak protection and to shore up the structure. Do not sandblast the old paint, as it may damage the underlying brick and mortar.