C.W.
I usually use the tube sucker upper (the detachable vacuum hose) on the vacuum, I have 2 cats and my mom has a dog so I have the pet hair vacuum. You can probably use a dust buster type portable device, but I've never owned one that was worth not throwing in the trash (they all sucked, figuratively because they actually didn't suck anything at all haha). It might be a pain because the vacuum hose only goes so far so i do lift it up steps every now and then to get everything, but looking at clean steps makes it worth it :)
Hope this answered your question. Wasn't particularly sure if you meant getting all the dirt off the stairs or deep cleaning (shampooing the carpet on the stairs)