After making and cutting the stringers, its time to start assembling the stairs.
Lay out and pour a landing pad, if required. Let the concrete cure. Mark the location of the stringers on the rim joist or header and fasten the stringers with angle brackets. Square the stringers to the deck frame and fasten them at the bottom with brackets. Then fasten a stair bracket at each tread location on the closed stringers, keeping the top of the flange lined up with the tread line.
Continue fastening stair brackets at each tread location on the open stringers, keeping the top of the flange lined up with the surface of the cutout. To help keep them flush, set a 2x4 scrap on the cutout, push the bracket under it flush, hold the bracket securely, and drive the fastener. Installing treads will go faster with one person under the stairs and the other holding the treads in place.
Measure the opening between the stringers and cut the first tread to length. Slip the tread in place and drive the fastener through the bracket into the underside of the tread.
If you're working with open stringers throughout the design, measure and cut your tread stock so it overhangs the stringers by 1-1/2 inches. Fasten the treads to the brackets.