I clad a stairs many moons ago, long before I had any machinery. I clad the risers in a layer of ply then veneered ply this packed the risers out so that they were flush with the nosing of the treads. I then had a local supplier machine up some hockey shaped boards which actually proved quite economic. It was then just a case of carefully cutting and planing each tread to size and fixing it down. It is still going strong 15 years later.
Whilst doing this I also clad the stringers. I made up a cardborad template and cut out the thinest veneered ply I could find. I fitted this before doing the treads so that they covered up any gaps.
James