Remove drywall boards to expose the studs of the wall where the floating steps will be installed. Measure the width between the studs.
Cut 2-by-4s to fit between the studs at each spot where a stair tread will meet the wall. Drill three pilot holes for lag screws in the face of each 2-by-4 for connecting the stair treads. Install the 2-by-4 supports by putting 3-inch screws through the studs and into the ends of the lumber, at the appropriate height for each stair tread.
Install the railing at the top of the staircase. Create a strong anchor point at the bottom of the staircase by attaching a good-sized banister, such as a 4-by-4 piece of lumber or thick wrought iron, directly into the floor. Connect the railing to the banister.
Drill holes for two railing spindles in the end of each stair tread that will be exposed.
Attach the first stair tread to the wall by installing lag screws at least 4 inches long through the 2-by-4 supports and into the tread. Make sure the tread is level.
Connect two spindles to the railing. Insert the spindles through the pre-drilled holes in the tread. Attach each spindle with a washer and lag screwed from the bottom or with a decorative washer and lock nut, if the spindle is threaded.
Install stair treads one at a time, moving up the staircase. Confirm the treads can support the necessary weight. If not, additional support may be needed in the form of a beam connecting the middle of the staircase to the floor.