Stairs consist of three parts: the stringer, the riser and the tread. The stringer is the part of the structure that actually supports the stairs (there are at least two stringers--one at each side of a stairway). The riser (the rise) is the height of an individual stair and the tread is the width of the stair.
Total rise is the vertical height from the landing to a point level with the height of the upper floor.
Total run is the horizontal length of the stairway, measured from the end of the staircase on the landing to the edge of the upper floor (or deck or porch).
Calculate the total rise. Put a 2 x 4 on the deck, then check that it's level with a carpenter's level. Measure from the bottom of the 2 x 4 to the ground.
Calculate the number of steps. Divide the total rise by 7.25. (7 1/4 inches is generally considered a good riser height). Round your answer up to the next whole number to determine the number of steps in your stairway. (Say the total rise is 64 inches and when you divide by 7.25 you get 8.8, which you then round up to 9. This is the number of steps you will need in your stairway.)
Calculate the total "run." Remember, on a stairway when you go up or down, the last step is either the ground or the deck surface, so you need one less tread than riser. Therefore, in this example with 9 risers, you will only need 8 treads. Since a standard tread width is 11 inches we would need 8 (the number of treads) multiplied by 11 inches (the width of our individual stairs), giving us an overall run of 88 inches.
Before you can lay out the stairs on the stringer, you need to calculate the exact height of the risers. You originally used the measurement of 7 1/4" to determine the number of risers as being 9, but that 7.25 inches isn't the riser height. Determine the exact height of the individual risers by dividing the total rise (64 inches) by the total number of risers (9). In this case, the actual height of each riser will be 7.11 inches (64 divided by 9), so use 7 1/8".
Use a framing square to lay your stairs out on the 2 x 12 stringers. Using the numbers on the outside of the square, mark the long arm with a piece of masking tape at 11 inches and the shorter arm at 7 1/8 inches. These are your rise and run calculations.
Position the long end of the framing square toward the end of the board and line up the two marks with the edge of the board facing you, and mark the outline of the square.
Slide the framing square up to the top mark, align the markings and again mark the notch. Continue marking and sliding up the length of the stringer.
Use a circular saw to carefully cut along the marked lines. Stop well back of the corner mark, and finish the cut with a handsaw. (If you cut all the way to the mark on the surface, the circular saw blade will cut past the line, weakening the stairs).
Test-fit this first stringer in place to ensure your calculations and measurements are accurate and then use this stringer as a template for marking the other stringers.
Attach the stringers to the deck by toe-nailing or using joist hangers attached to the deck framing.
Starting at the bottom, install the stair treads using 3" nails or screws to fasten them.