Use a crowbar to remove the old treads from the stairs. You will need to place the crowbar between the tread (the main part of each step) and the riser (the veneer that rests over the vertical part of the step). Pull off each tread and use the crowbar to remove the risers as well. Check to make sure that the frame of the stairs is still sturdy and intact.
Cut a number of plywood boards to fit the staircase and put them over top of the old frame. Cover both the vertical and horizontal part of the stairs. The exact measurements of these boards are unimportant, but they should be strong enough to support your weight. The frame underneath the plywood boards should be made of construction materials, so you can use carpenter's glue or nails to secure the plywood boards.
Cut or purchase new treads and risers. Use the old ones as templates. Generally a tread should be 1 inch thick and the risers should be a quarter-inch thick. The length will depend on the space you have.
Lay your treads and risers over the frame to ensure that all the pieces fit correctly. Use a small handsaw to trim the stairs if need be.
Finish the treads and risers with a polyurathane coating. Let them sit for one to two days to ensure that the coating has set. A polyurathane coating will make the stairs sturdier and more attractive.
Affix the treads and risers to the plywood stairs using carpenter's glue. Start at the top and work your way down the staircase. Glue is the best option for the actual stairs, as materials such as nails will make the stairs look messy.