Buy your lumber at your local lumber yard or home improvement center. Pine is inexpensive and easy to work with, but it's possible to build this bunk using more expensive and attractive wood.
Cut your lumber to the dimensions listed using your power saw.
Sand all surfaces of your lumber. You don't have to get it polished smooth, but it should be smooth enough to avoid getting splinters or snagging the fabric of your futon. If you want to paint your frame, it's easiest to paint the lumber before construction.
Take one short beam and one long beam. Arrange them in an L-shape, with the end of the short beam against the inside face of the long beam. Screw them together with two 4-inch wood screws.
Repeat Step 1 to make a second "L" with the remaining beams.
Arrange the two L's into a rectangular frame. Screw the open corners together the same way you did the L's.
Set one plank at each short end of the frame. Their outer edges should line up with the outer edges of the frame. Screw them in position with two 2-inch wood screws along each 12-inch end of the plank.
Set the four wooden posts into the frame, one at each corner. Use six 4-inch wood screws to fasten each to the frame. Drive in two screws each through the short beam, the long beam and the post.
Arrange the remaining planks along the top of the frame, in between the two planks you've already installed. Space them evenly, leaving small gaps between for air flow. Screw each in place with two 2-inch wood screws along each end.