I did use a knee-kick stretcher and an electric stapler when I did my basement stairs.
I started at the bottom,stapled the first riser along the bottom,wraped up and around the nose of the first tread,then used the stretcher on the tread and stapled where the tread meets the next riser and so on up the stairs.
And I stapled the pad down first before the carpet other wise it may bunch up under the carpet.Luck