Summarize:

Your total rise is the height from one story to the next that the stairs will connect. The total rise should be set in most cases, so you simply need to measure the height. This distance should be from the top of the finished floor below and the finished floor at the top. If the floor is unfinished when you are calculating your stringers, you need to take that into account. The height of each step can vary a bit but there are general standards. It is standard to have your riser be about 7 inches (18cm) tall, so use this measurement unless you have specific parameters that prevent it, such as limited headroom. This measurement is sometimes called the individual rise of the stairs. For this calculation you are simply figuring out how many stairs it will take to get the height you need. Use a calculator or do the arithmetic by hand, as it is generally pretty simple. For example, if you want 7 inches (18cm) tall stairs and your overall rise needs to be 56 inches (140cm), then 56/7=8. You will need 8 stairs. The number of treads you have (individual runs) will automatically be one less than the number of risers. Your total run is the horizontal distance between the top and the bottom of the stairs. How far the stairs stick out can vary depending on your needs, but keep in mind that stairs should usually be at an angle of about 40 degrees. In general, the run of each stair should be about 10 inches (25cm) in order for people's feet to fit comfortably as they walk up them. There are many stair calculators that you can use online to figure out stair measurements. You simply need to input your rise and the angle you want for your stairs and they will calculate the other measurements you need, including your run. Once you have the overall rise and run of the stairs, you can calculate how long the stringer needs to be. You can either use an online stair calculator, a hypotenuse calculator, or you can do the math yourself. To calculate the length yourself, you will need to use the Pythagorean theorem, which is a2 + b2 = c2. So, for example, if the rise needs to be 60 inches (150cm) and the run needs to be 84 inches (210cm), then you would calculate 602 + 842 = c2, with "c" being the length of 99 inches (250cm). Ensure your math and calculations are correct so that you don't waste your time and materials cutting risers that don't fit. It's better to take a few minutes to double check yourself than to waste a whole lot of time redoing your work.
Measure out how much total rise your stairs need. Determine how tall you want each step to be. Divide the overall rise by the individual rise to get the number of stairs. Determine how much run each stair will need. Calculate how long the stringer needs to be. Double check your measurements before you start marking your cuts.