I was looking for something else in my Readers Digest fix-it book and found this:
"Winding stairs require folds in the carpet to take up slack at the narrow point of the stairs. With stair rods, fold the slack down toward the lower stair rod and drive three tacks through the doubled carpet across the width of the fold, working from the broadest to the narrowest part. Pull the carpet taut. Position the next tread and repeat. With tackless fittings, nail a flat metal grip to the tread of the first step to hold the carpet. Stretch the carpet over the tread, swinging it around to follow the turn of the stairway. Fold the resulting slack downward to meet the flat strip just installed. Mark the back of the carpet at the base of the fold on both sides. turn the carpet back down the staris, holding the two marks well into the angle where tread and riser meet. Secure the fold with a second flat strip nailed into the riser through a double thickness." There's a small diagram in the book which I think does better than the words. Maybe you can find a current Reader's Digest book; mine's 1970s version.