I drag out my canister vacuum for stairs. Set it up at bottom of stairs, attach hose and work up the stairs. I find the hose has enough suction to get that "corner" between the stairs and risers clean. And that's important with a dog and a cat in the house. Good luck!

Vacuum bottom to top using the hose and a head with no brushes and use the crevice tool for the corners

There is nothing like a hand held vacuum or a small canister that can be set on end for stairs. I have a small ureka that I use. I bought it for $89. You need one that has all the tools with it. No heavy vacuum to lug and you have the brush and crevice tool on hand to give it a good cleaning

great tip given to me by a housecleaner once was to use a large, slightly damp sponge and rub steps to get off dog/cat fur(after vacuuming if the steps have dirt on them)....works really well!

A small hand-held turbo brush with any sort of vacuum cleaner (I now have a cannister, but used to have an upright) is the best solution I have found. A long vacuum hose makes it easier. And we have a sweet, otherwise perfect, golden retriever who sheds like crazy.