Intro
You can refresh your old staircase with new treads and risers. Wood replacement treads are available that can be secured directly over the existing "subfloor" treads and risers. The "body" of these replacement treads is 1/2 inch thick so that your steps will remain a consistent height. The nose on the replacement tread is 1 inch thick to retain the illusion of a standard tread.
You can also opt to remove the old stair surfaces and begin anew as shown here. Select a wood type for the new treads and risers that will complement flooring and moldings in the rooms the stairs adjoin. Standard stair treads come with a rounded (bullnose) front edge and measure 1 inch thick and 11-1/4 inches deep. Plan to measure the width of each stair because each one will vary slightly in width.
Stairs that are enclosed on both sides (with no balusters) are a job you can do yourself. For anything more complicated plan to hire a finish carpenter to do the job.
Prestart Checklist
Time
About 1 hour per step
Tools
Measuring tape, power saw, compass, pneumatic nailer
Skills
Measuring, scribing, and using a power saw and pneumatic nailer
Prep
Remove old stair surfaces if desired
Materials
Stair treads, risers, wood putty