Cover any trim with painter's masking tape.
Wash the wall with trisodium phosphate and a rag (see Reference 2, pg. 188). Your new paint will cover the Frazee wall paint in fewer coats if the surface is freshly cleaned.
Prime the Frazee wall paint with general-purpose primer if you are painting over oil-base Frazee paint. Oil-base paint does not cover easily without primer (see Reference 4, pg. 67). Most interior wall paint is water-base latex paint with a flat finish, but if you're uncertain, prime just to be on the safe side (see Reference 3). Use a paintbrush to prime the edges of walls, and a roller for larger wall areas. Wait for the primer to dry before proceeding.
Paint the wall using any interior paint. Use a paintbrush for edges and a roller for main wall surfaces.
Apply a second coat of paint after the first coat dries. Your new paint application should cover over the Frazee paint in just one or two coats, but if you're going from a dark color to a light color, it may take upwards of three coats.
Remove the painter's tape after the final coat dries for 24 hours (see Reference 5, pg. 185).