Remove the carpet, padding, and tack strips from the stairs and throw away. Use pliers to remove all tack strips and staples from the stairs.
Place the sandpaper on the electric sander and sand the top and front of each step. Remove the dust from the stairs by using shop vac making sure you get all of the dust and dirt off of them and wipe with a dry clean cloth.
Apply stain to a clean rag and stain every other stair treads and then the landing. Allow to dry for 2 days or per stain can instructions. Apply stain to the remaining stairs using a clean rag and allow to dry for at least 2 days.
Apply Polyurethane using a clean synthetic bristle brush on every other stair and landing and allow to dry according to can directions but usually at least one day. Apply Polyurethane to remaining stairs and allow to dry for at least one day.
Cut beadboard to fit the rise of all stairs. Paint the sides of the stairs tapping off the ends. Paint the boards that you made for the rise and install with a nail gun after they dry. Touch up paint where you used the nail gun.
To clean, use a broom to get the dust off and the use a steam mop.
Notes
Although your landing may have the right piece of wood, our landing was not suitable for refinishing the wood so we had to cover it and install an ⅛" plywood and then finish it.