Stairs are the part of a deck most likely to be built badly, and a bad stair can hurt someone, so go slowly. Limits here come from the 2021 IRC and the American Wood Council's deck guide, DCA 6.
1. Measure the total rise where the stairs land
Measuring down from the deck at the house gets people in trouble, because yards slope. Run a level or a laser out from the deck surface to the spot where the bottom tread will sit, then measure straight down. Ground that falls 3″ along the run adds 3″ of rise. Since the bottom of the stair moves out as you add steps, you may need to measure twice.
2. Work out risers and treads
Our rise is 40″. Divide by the 7 3/4″ maximum: 40 ÷ 7.75 = 5.16, which rounds up to 6 risers. Then 40 ÷ 6 = 6.67″, or 6 11/16″ on a tape. A stair always has one fewer tread than risers, because the deck itself is the top step, so that's 5 treads.
Two 5/4×6 boards with a small gap make an 11 1/4″ tread. Five of those take 56 1/4″ of run, so the stairs land 4′ 8 1/4″ out from the deck. Make sure nothing is in the way there and the ground is close to level.
The stair calculator does this and checks it against code. If you'd like gentler steps, add a riser and see what it does to the run.
3. Lay out the stringers
Use 2×12s, the minimum in DCA 6. The notches leave a strip of solid wood behind them called the throat, and the guide requires at least 5″ of it. A 40″ stair with 11 1/4″ treads leaves about 5 1/2″.
Set stair gauges on a framing square at 6 11/16″ on the tongue and 11 1/4″ on the blade. Starting at one end of the board, trace each notch, sliding the square along so the gauges ride the edge. You can pull the same numbers for your own stair from the stringer calculator, along with a drawn layout to check against.
The step people miss is dropping the stringer. Your treads sit on top of it, so without a correction the bottom step would be too tall by one tread thickness and the top step too short. Cut that thickness off the bottom of the stringer. With 1″ treads, the first riser becomes 5 11/16″.
4. Cut and test one stringer
Cut with a circular saw and stop short of the corners, then finish with a handsaw or jigsaw. Running the circular saw past the line weakens the throat. Hold the stringer in place, check that the treads are level and the top meets the deck correctly, and only then use it as a pattern for the rest.
5. Attach it at the top and bottom
At the deck, DCA 6 shows sloped joist hangers rated for at least 625 pounds. Toenails alone won't do. At the bottom, DCA 6 attaches the stringers to the stair guard posts and sets them on a 2×4 bearing block fastened to each post. Those posts stand on footings at least 10″ square or 12″ round and 6″ thick, placed 12″ below undisturbed ground or below the frost line, whichever is deeper. Never rest stringers on bare dirt, and ask your building department before you swap the posts for a concrete pad.
Cut stringers can span at most 6′ 0″ horizontally under DCA 6, and our 56 1/4″ run is well inside that. Longer stairs need a 4×4 post under the stringer, solid stringers or a landing. Any stair more than 12 feet tall needs an intermediate landing.
6. Fit treads and rails
Stairs must be at least 36″ wide. With 5/4 or 2× treads, DCA 6 calls for two #8 screws at least 2 1/2″ long, or two 8d threaded nails, per tread at each stringer. On a tread made of two boards, put two in each board so neither one can lift.
Our stair has 6 risers, so it needs a handrail between 34″ and 38″ above the nosing. At a 40″ rise it also needs guards. Deck stairs usually need a permit and inspection, and local rules can differ, so check with your building department. If the deck itself isn't built yet, the deck calculator will count boards, joists and screws for it.