There are four basic ways a circle skirt is cut. Depending on the hem width required it goes from 360° to 90°. For countless folds the double circle construction can be used - cut to circles with half the waist girth each and sew them together. Now twirl girl, twirl!
Circle skirt works best when done with lightweight flowing fabric. The soft folds along the hem without much bulk around the waist line is the main characteristic of this skirt. Another is the simplicity of its construction. I made my first one in the third grade, and proudly worn it all summer holidays.
Common problem with the this skirts is the uneven hemline. Sometimes it only appears after a wash or two. It accrues because skirt is cut disregarding the fabric grain. The inconsistent stretching becomes apparent only after water and heat treatment. To a certain extend it might be compensated when the pattern is cut. The big question is where. Some say at the hemline, others, prefer to do it at the waist. There are too many variables to give the universal advice. Just go with your gut feeling and experiment.