Place a large throw rug over the shag carpeting to minimize how much of it is seen. This also gives you freedom in choosing a color scheme, since throw rugs come in a variety of colors and styles.
Use furniture such as tables, couches, dressers and chairs to cover shag carpeting at the sides and center of the room.
Lay down a rubber mat in high-traffic areas. Rubber prevents people from slipping, and it hides the carpeting underneath.
Pull up the shag carpeting in any uncovered areas. The bare floor may be more aesthetically pleasing than the shag carpet.