If your hardwood overlay arrives unfinished, you have the option to glue as well as nail or screw down the wood. Using two attachment methods reduces the chance of movement between the plywood and hardwood, and lessens the likelihood of annoying creaking when the stairs are in use. Standard construction glues such as those labeled for subfloors and decks, are fine for dual method attachments. These glues are available in easy-to-use tubes that attach to a caulking gun.
With pre-finished hardwood, you do not want to use nails or screws at all since they will mar the factory-applied finish. If you are creating a finished step without top-nailing, choose a urethane spread adhesive that can be uniformly spread with a trowel. Look for a trowel notch size that provides coverage of 50 square feet per gallon. A hardware or home improvement store can assist you with glue and trowel selection for your project.
Most construction-type glues are not easily removed once they have set. Use caulking tubes cautiously and squeeze out the adhesive slowly and gently. Spread out thick areas for even coverage. Urethane-based glues can be very messy. Keep a rag infused with mineral spirits nearby to keep finished wood surfaces clean as you work. For smaller areas where joinery accuracy is an issue, use a quality wood glue that will create a uniform surface.
Rather than finishing your hardwood steps after they have been installed, custom-fit the hardwood on your roughed-in stairs, label the underside of each board according to location and finish the treads off-site. Apply urethane adhesive and the job is finished. For stair treads, ask your supplier for a stair tread adhesive. This glue not only holds the tread in place, but also works as a buffer to prevent squeaks.