For me, it depends on the fabric & the soil level as well as the type of soil, ie; water soluble or oil based.
Upholstery:
I mainly use my Makita Variable speed polisher after vacuuming the furniture.
This is then pre-sprayed with my choice of solution.
I use various bonnets under the Makita, replace each one before they start to get too soiled.
Each piece is then toweled off to remove any remaining soil and also to help dry the fabric as well as leaving the pile laying in the same direction if it is a cut pile.
By toweling off, I can also see when the fabric is clean.
This could be the "extraction" process compared to water extraction.
I do have a water based solution that I use on oil based soils.
With extremely soiled pieces, I will also rinse/extract after agitation with the Makita.
Sorry, I don't have a photo of my Makita.
Stairs:
Again, I use a couple of different methods.
Depending on how I see the stairs, I will use my Cycle Orbital Polisher from Hos with two brushes on, this comes with an extension handle which allows me to clean whilst standing up.
The Hos Micro used to come with two handles when I bought mine, I believe that it now comes with only the short one (NO PUN), I only carry the short one as it also fits into my tool box along with the machine, spare brushes and pads.
After vacuuming, I pre-spray, starting at the base, I do the risers until I reach the top, then come back down spraying the treads.
I then have the Cyclo pointing away from me and clean the risers, again starting at the base & going up to the top.
I then stand 2-3 steps down from the top step and clean the treads as I come down.
I will also towel the treads and sometimes still even will extract.
Other times I will use my Oreck 12" orbital, but I don't find this as easy as others here do.
Don't have a photo of the Oreck either.
Hope this helps and puts a smile on your face.
I don't regret my past, I just regret the times I've wasted with the wrong people.
Take me as I am, or watch me as I go.
I'll retire when I can no longer do what I love, or I no longer love what I can do.
Stop moving, start dying........