Even if your walls are curved rather than straight, it's still possible to install carpet. Curving a carpet edge also allows installation of carpet to meet up with curved tiled or hardwood floors.
Prepare the tack strips and carpet padding
Use a utility knife to trim tack strips into small pieces. Place the pieces on the floor with the teeth facing the wall and the ends of the strips touching each other. Hammer the tack strips into the floor. Lay carpet padding down on the floor. Cut the padding around the edges so that the ends of the padding touch the tack strips but don't cover them.
Lay down the carpeting
Unroll the carpeting over the padding, pushing it against the curved walls. Fold the excess carpeting up with the underside of the carpeting visible. Cutting from the underside, trim the carpet so there is a 3-inch margin beyond the tack strips. Push the carpet down around the curved walls. Fold and trim each section of carpet as you reach it. Use a knee-kicker to pound the carpet down onto the tack strips. Use a stair chisel to push the carpeting into the teeth of the tack strips.
Trim the carpet
Work your way around the curved walls once again, trimming any excess carpet with a utility knife. Measure and cut molding to cover the points where the carpet meets other types of flooring, and hammer the molding in place.