I always use a good quality tube adhesive such a “Liquid Nails’ or one of the Bulldog brands. Always make sure that the tread fits easily without having to force the wood into place and keep every one off for 24 hours. Its nice to have the ends available to tack the piece into place but it is’nt necessary.
I start by cutting and fitting the wood for both the risers (if desired) and treads, starting at the top of the stair case working down. Be sure to stack or label everything in sequence. At the end of the day, when I can close the stairs to traffic, I start back at the top of the stairs, edge nailing and gluing the pieces where I can and only gluing where necessary (such as the nosings).
I once had to remove the hardwood strip flooring from a number of treads after the movers skidded a piece of furnature down the stairs and I had to literally shred the wood to get it off. I’ve been using this method for 16 years and have not had one call back due to my craftsmanship.
-- Jim, Alberta Canada