Before you can retread steps, you must remove the stair spindles. You may also want to remove stair spindles for easier painting. Wood spindles have a dowel pin that holds its base to the underlying stair tread. The handrail has fillers that hold the tops of each spindle in place. Metal spindles have screws that hold them to the stair treads and the underside of the handrail. Little removable covers hide these screws. The job shouldn't take more than a day to complete.
Lay a thin hand saw blade on the tread of the stair so that its teeth are where the bottom of the spindle and the top of the tread meet. A little wooden dowel pin connects the two together. Move the saw back and forth to slide under the spindle and cut the dowel pin. Repeat this process for each spindle.
Walk to the top of the stairs and look between the first spindle and the newel post (the newel posts are the main posts that support the handrail). Look underneath the handrail and you'll see a short piece of filler wood pressed in between the spindle and the newel post. Pry this piece out with a flathead chisel. Use a hammer to hit the back end of the chisel to help get it out, if necessary. Be careful not to break the handrail edges.
Pull the top of the spindle toward the top newel post to slide it out of the bottom groove of the handrail. Repeat this process all the way down to the bottom spindle. Some spindles may have been tacked in place with glue, so you may have to pull on these with a quick tug to get them free.
Lift the decorative covers up off the bottom of the spindle base where it connects with the stair tread and down from the top of the spindle top where it connects with the handrail. This will expose the screws.
Remove the screws from the top and bottom of the spindle with a flathead or crosshead screwdriver, depending on the type of screws used.
Pull the top of the top spindle at the top of the staircase toward the newel post and remove it. Repeat this process until you've removed all spindles down to the bottom newel post.
If you break one of the wood fillers that hold the wood spindles to the underside of the handrail, they aren't too expensive to replace.