On stairs that just need a light extraction, I use a 6" stair tool (the short version with grab handle on top) ... I find these tools a bit cumbersome tbh, and they cause back-ache.
When stairs are dirty and need a good rinse through I use a 3.5" hand tool with an 03 jet. I find I naturally space my passes out too much with the 6" tool and can leave stripes on occasions.
If the risers look quite clean, they just get a misting of water from the jet and then I turn the tool upside down and go up and down along it from end to end.
To do the nosings... with the 6" tool make sure your extraction stroke comes far enough back so the water hits the nose, let go of the trigger and pull it round the curve a little, before pushing forwards for your next stroke. With the hand tool, simply extract along the stair nose with the tool held at about 45degrees blocking off an inch or so of the vacuum slot with your finger, to retain suction on the carpet (mind your fingers in the hot water

). The thicker the pile the easier it is. Do the same with the 6" tool for a dry pass, angling the tool sideways a bit.
I'm boring myself now so I'll stop
