Lay a 6-foot-long straightedge flat on the concrete. Slide it across the floor in all directions, circling the low spots on the concrete with chalk where the straightedge does not touch the floor. Low spots require additional support under the sleepers.
Measure the thickness of a 2-by-4 board. Measure from the floor up a wall to that measurement, and mark the wall with a pencil. Repeat at several locations around the room on each wall.
Place a straightedge against a wall, aligning it with the row of pencil marks. Trace the straightedge with a pencil to connect the marks into a solid line. Repeat around the room until there is a continuous line across each wall.
Pull out several feet of the chalk line and attach the small level to the line. Most chalk-line levels hang from the line with two hooks.
Hold the free end of the chalk line at the pencil line on one wall. Ask a helper to pull the chalk line across the room to the pencil line on the opposite wall and pull the line taut. Because the floor is not level, the bubble in the chalk line cannot be centered.
Adjust the lower end of the chalk line up the wall until the bubble inside the level is centered. Mark the position of the raised end of the line on the wall with a pencil.
Move the chalk line along the pencil lines on opposing walls, and repeat the leveling process.
Connect the new, level marks on the walls by tracing the straightedge until you have a level pencil line surrounding the room.
Lay the 2-by-4s in parallel rows on the floor, spacing the rows 12 inches apart. In rooms that are longer than one 2-by-4, measure the space from the end of the last board of a row to the wall. Apply that measurement to another board. Cut the board with a circular saw and set it in place to finish the row.
Slide asphalt shingles under the boards, raising the sleepers to meet the level line on the walls surrounding the room. If one shingle does not raise the board to meet the pencil line, stack two or more shingles under the boards.
Inspect each row for gaps underneath. Slide shingles into any spaces for extra support. This prevents the sleepers from bowing underfoot.
Place a 4-foot level on a row of sleepers. If the bubble is not centered, add or remove shingles as necessary to make final leveling adjustments. Repeat along every row of sleepers.
Drill straight through the sleepers and into the concrete to a depth of 3 1/2 inches with a hammer drill and a 1/4-inch masonry drill bit. Space the holes approximately 6 inches apart along the center of each board.
Hold two 16-penny nails together, side by side, and place the tips of both nails into one drilled opening in a sleeper. Drive both nails together through the pre-drilled hole and into the concrete with a framing hammer or small sledgehammer. Continue throughout the room until each sleeper is fastened to the concrete.