Sure, building stairs looks complicated, but appearances are deceiving. Stairs are formed with stringers  generally 2by10 or 2by12inch boards  cut to accommodate specific measurements. Called the run for the depth of each step and the rise for the height, from one step to the next, these are calculated mathematically based on the total rise of the stairs  the distance from one level to the next  and the total run  the distance the stairs extend outward. Attention to detail and a calculator, along with a few boards, is about all you need to build your own competently.
Things You'll Need
 Tape measure
 2by12inch boards
 Carpenter's square
 Straightedge
 Wood clamps or tape
 Circular saw
 Handsaw
Calculating the Rise and Run of Each Step

Measure from the upstairs, at floor level, down to the basement floor. Ensure the tape measure runs straight down for accurate measurements. Record the result in inches as the total rise for the stairs.

Divide the stairs' rise by seven to determine the number of steps you need for your stairs. Seven inches is considered the ideal step rise, according to the International Building Code, upon which all local building codes are based. Thus, a span of 7 feet 3 inches  87 inches  divided by 7 results in 12.4 steps. Round your result, either up or down, to obtain a whole number if the rise is not evenly divisible  in this case, 12 steps.

Determine the step rise by dividing the total rise, again, by the number of steps needed. For instance, in the previous example of an 87inch total stair rise, 87 divided by 12 yields 7.25 inches. Each step is therefore 7 1/4 inch above the previous step  very close to the ideal 7inch rise.

Find the step run necessary for your stairs. The IBC recommends a minimum of 11 inches; builders use the rule of thumb that the rise, in inches, plus the run, also in inches, should equal 18 to 20 inches. Thus, with a step rise of 7.25 inches, a step run of 11 inches is within standards. Increase the number slightly to create a deeper step.

Multiply the number of steps in the stairs by the run desired to find the total stairs run. For example, in the previous example with 12 steps, an 11inch run results in a total run of 132 inches in length, while a 12inch run produces a total run of 144 inches, in contrast.

Apply the Pythagorean Theorem to obtain the stair stringer length needed. Picture the total stair rise as one leg of a right triangle and the total run, just calculated, as the other leg. The stringer is the hypotenuse. Thus, square the total rise and square the total run. Add them together. Find the square root of the sum to determine the stringer length.
Given a total rise of 87 inches in the previous example and choosing a total run of 132 inches  reflecting a step run of 11 inches  the stringer length is: 87 times 87 equals 7,569, and 132 times 132 is 17,424. Added together, these equal 24,993. The square root of 24,993 is 158.09. Rounded, this results in 158 inches.
Cutting the Stringers

Lay a large carpenter's square flat with the point formed at the middle facing away from you. Align a straightedge  a small strip of wood, ruler or anything handy  with the step run measurement on one leg of the square, and with the step rise with the other end. Tape or clamp it in place to secure. The end result is a complete triangle shape that outlines the steps precisely.

Align the triangular square with the edge of a 2by12inch board, cut to a couple inches longer than the stringer length needed. Turn the square so the rise measurement is closest to the end of the board, to create a rise first. Allow the bulk of the square to rest on the stringer with the straightedge guide sliding along the edge of the stringer.

Trace, from the beginning corner of the stringer, along the right leg of the triangle created with the square, to outline the step rise, then along the left leg, which marks the step run. Slide the square down to the ending of the run just marked and repeat. Continue down the length of the stringer, creating a zigzag pattern.

Cut the stringer, following the outline, using a circular saw, until you reach the inner portion of each step. Switch to a handsaw to sever the final inch of each step, near the back of the step run. This avoids cutting deeper than necessary, which weakens the stringers significantly.

Place the completed stringer on top of another stringer, cut to the same length. Outline the stringer to create the pattern on the opposite stringer. Cut similarly. Repeat for any other stringers needed; generally, one stringer for each 16 inches of stairs width is desirable.

Measure down, from the first step on the stringer, the step rise plus the thickness of the boards used for tread. For instance, with a 7 1/4inch rise and 1inchthick boards covering the step, find the point 8.25 inches below the first step. Mark a straight, level line across and cut. This squares the bottom of the stringer and creates the perfect height.
Tips & Warnings
 Consult your local building department for code requirements for your stairs. Codes vary from location to location. Among other specifics, your local code will govern measurement ranges and railings, along with the head space required, which is created when the stairs opening is cut.
 Cut boards for treads  the actual step  and risers  the backs of the steps  to complete the stairs. Set the treads first, allowing the riser to rest on top of the rear edge in a butt joint. Nail to the stringers to attach.
References
 Photo Credit Ryan McVay/Lifesize/Getty Images