Without a bed frame, your "bed" is nothing more than a mattress and box spring placed on the floor. Frames are typically made of either metal or wood and can either have built-in supports to prevent the mattress from falling through or require you to add slats for support. Instead of searching around at furniture stores, save yourself money and build a slatted bed base. The materials are available at local hardware stores.
Cut your 2-by-4 pieces of lumber into 4 individual boards, with two measuring 80 inches long for the sides and two measuring 57 inches long for the top and bottom. A lumber yard may cut the boards for you if you bring the lengths with you when you purchase the wood.
Lay your boards in a rectangle to form the basic shape of the bed base with the top and bottom boards on the inside of the two sides. All boards should be on the smaller 2-inch side.
Drill wood screws into each of the four corners of the rectangle. Drill from the sides of the rectangle toward the center, with the screws going through the sides of the base into the top and bottom boards that form the base.
Cut the 1-by-4-inch boards to form slats on the base to support the mattress. Each slat should measure 61 inches long so it can secure to the top of the basic rectangular base. Cut five slats.
Place the slats at 15-inch intervals along the length of the base, laying each one on its long side. Secure each slat to the base with wood screws on each side.
Place a post in the corner of the base where the two beams meet. Drive wood screws through the bottom-most slat directly into the post. Add reinforcement with two wood screws through the short beam and two more driven through the long beam directly into the post. Repeat for the other three corners of the base.
Add another post halfway down each side and in the center of the top and bottom beams. Drive wood screws straight down through the slat that lies directly above the post. Increase support with three more wood screws driven through the beam the post lies against.