Understanding the stair construction is the key element in getting the right measurements of them. Depending on the type of a staircase the measurements goes differently. For example, for a straight staircase the distance from the finished floor level (where the staircase starts) to the finished floor level on the upper floor (where the staircase is going to) is a rise measurement. Going distance is the distance the staircase will project along the floor, and for the width measure the narrowest point between walls…  All of this should be transferred on the 2D image that will make a clear visual scheme of the situation. For more option and other types of staircase measuring, read further in the link bellow.

Source.

...