Wood – How to avoid squeaking with a hardwood floor

If you are going to salvage your floor, that is, try to set your new stairs with its landing nosing to meet the original floor, you need to make a rough cut with a carbide saw blade say about a 24 tooth blade. This cut is to be made smaller than you need at first to find the limits the stair will fit. After the area is checked for how the framing is in the area and the place is determined where the nosing will stop against the original floor, that cut is made with a new carbide tipped blade, if the other blade found nails. If a nail is found with the new blade, cut through it, then change to a new blade and continue cutting until another nail is found, then replace the blade again.

If you are going to do a new floor "tie in" and flooring is to be reset anyway, then the final cut does not need to be this critical. If you are getting floor installers to do the tie in, they will cut back, tooth in, all that for you. Just make sure the landing nose is securely set at the stair.

This is a start, other will factors determine how to cut the floor to make the install of stairs simpler, that would take photos of the area in question. As in, is it a stair well closed on the sides, or a open stair well with the new stairs exposed to the room to start?

If the scratches are all in the finish rather than gouging the wood, then (depending on what finish is already there) a "screen and re-coat" pass might be another option. That approach just roughs and somewhat levels the surface of the existing finish, then lays down a fresh coat on top of it. Faster and cheaper, can yield good results if the floor's basically in good condition, doesn't cut into the "wear layer" of laminate flooring as much as a full refinish would... but won't take out any deeper damage and may not be applicable for all finishes, especially if they've had polishes/waxes applied on top of them.

(I just know it's an option, can't advise on details. Personally, I sorta like the fact that some of my floors have clearly been in use as long as the house has stood here; as long as there's enough finish to protect the wood and it's clear enough to let me see the wood, I'm happy.)

Unless you want to darken the wood, I wouldn't consider staining unless necessary to match color in a damaged area... especially since you have to strip ALL the varnish off first or the stain will go down unevenly. Remember that wood looks different dry than it does either wet or under a varnish (try wiping it with denatured alcohol to get a better sense of what it will look like when varnished). Also remember that the varnish may add some color of its own, depending on what you use.