Place the first tread in position. Depending on the type of stairway you have, this could involve sliding it into notches in the stringers or setting it on top of the edge of the riser. The stringers are the diagonal pieces of wood that support the stairway. The risers are the vertical pieces of wood that fill the gaps between the treads.
Crawl under the stairs and draw a pencil line on the bottom of the stair tread, following the inside edges of the stringers and the riser. Use a flashlight so you can see what you're doing.
Remove the tread and set it upside down on a workbench. Position pieces of 3/4- by 3/4-inch wood against the bottom surface of the tread so that their edges align with the lines that you drew, with the pieces of wood toward the inside of the tread.
Screw these pieces of wood onto the tread by drilling a pilot hole through the wood and into the tread, then screwing in a 1 1/4-inch-long screw. The pilot hole should be 1/32-inch larger diameter than the screw threads. Only drill until the tip goes into the tread, so that the screw will slide through the wooden cleat but bite into the wood of the tread, drawing the two together tightly. Drill a hole for a screw every 6 inches along the length of the wooden cleat.
Replace the tread in its position on top of the riser and the stringers.
Crawl back under the stairs and screw the pieces of wood that you attached to the tread to the riser and stringer by drilling a pilot hole horizontally through the wood, then screwing in 1 1/4-inch-long screws. Place a screw at the center of each space between the screws that you put into the tread. The screws that go into the riser and stringers will then be spaced 6 inches apart.
Repeat this process for every stair tread that you want to install.