This is the stepbystep, printable version. If you PRINT this page, any ads will not be printed.
See also the animated version.
After doing this  Your work should look like this 

We start with the given circle, center O.
Note: If you are not given the center, you can find it using the method shown in Finding the center of a circle with compass and straightedge. 

1. Draw a diameter of the circle through the center point and mark its endpoints C and M. It does not have to be vertical.  
2. Construct a perpendicular to CM at the point O. For more on this see Constructing a perpendicular at a point on a line. 

3. Mark the point S where it crosses the circle.  
4. Find the midpoint L of the segment SO by constructing its perpendicular bisector. For more on this see Constructing the perpendicular bisector of a line segment. 

5. Set the compasses on L, adjust its width to S or O, and draw a circle.  
6. Draw a line from M, through L so it crosses the small circle in two places. Label them N and P.  
7. Set the compasses on M and adjust its width to P.  
8. Draw a broad arc that crosses the given circle in two places. Label them A and E.  
9. Set the compasses on M and adjust its width to N.  
10. Draw a broad arc that crosses the given circle in two places. Label them B and D.  
11. Draw a line from A to B, then B to C etc, until you have drawn all five sides of the pentagon.  
Done. ABCDE is a regular pentagon inscribed in the given circle. 