At the location where the stairs will contact the landing, place riser stock (plywood) to create a connection point for the stringers (Image 1).
Place the stringers in place and on your layout marks. Fasten from behind the riser stock (Image 2).
Install riser material on the stringers. Cut each one exactly the same so the stair is the same width at all points (Image 3).
To really fasten the treads, glue and screw them down (Image 4). This prevents squeaks and makes a permanent bond.
Use screws, rather than nails, to fasten tread stock to the stringers (Image 5). Screws will form a tighter bond with the glue.
Sink screws from behind the riser stock into the edge of the tread (Image 6). This binds everything together into a unit.