Buy lumber at a home improvement center. Pine and plywood are the least expensive and most forgiving wood options, but you can choose more expensive wood for a fancier finished product.
Cut your lumber to the dimensions listed, using your power saw.
Drill two holes in each end of all four of your 84-inch beams. Make the holes on the center line of the 4-inch face of the beam, placing the holes 1 inch and 2 1/2 inches from each end. Use a drill bit the same diameter as the shafts of your lag bolts.
Drill four holes in each of your posts, in two sets of two. Drill the holes 1 inch and 2 1/2 inches from one side of the post, using a drill bit the same diameter as the shafts of your lag bolts. Place one set of holes about 6 inches from one end of the posts. Place the other set about 18 inches from the opposite end.
Sand all faces of your lumber.
Arrange two of the 36-inch beams and two of the 84-inch beams together in a rectangular frame. The shorter beams should abut the inside faces of the long beams, with all beams resting on their 2-inch edges. Place the short beams so their outside edges are 4 inches from the ends of the long beams, making the frame resemble an old-fashioned bed litter.
Screw the beams in place using two 4-inch wood screws at each corner. Drive the screws through the face of the long beam and into the end of the short beam at each point.
Place one wood sheet over the frame so that its corners align with the points where the short and long beams meet. Screw it in place with a 2-inch wood screw at each corner.
Repeat steps 1 through 1 to build the second bunk frame.
Set the four beams up in the room where you want the bed, one beam per corner. Set them so that the end that's 18 inches from the holes is the end closest to the ground.
Set one bunk frame in the middle of the beams. The forks protruding at each end should fit around the beams at each corner.
Slide the bolts through the holes in the bunk frame and the beam and then tighten them down by hand. This step is much easier with at least one person to help you .
Repeat steps 2 and 3 to bolt the upper bunk into place.
Use pliers or vice grips to tighten down all bunks until the frame no longer wobbles when shaken.