Using the ellipse tool
The ellipse tool allows you to draw ellipses and circles on your image. By default, it draws a pixel-wide border around the ellipse, but this can be changed in the ellipse tool's properties window:

The drawn ellipse can be either filled or unfilled. If you choose the first option for the fill color, whatever color is set to the mouse button you're using will be used to fill the ellipse. The second option gives you the opportunity to use an alternate shade for the inside of the ellipse.
Additionally, you can set the width of the border drawn around the ellipse by altering the field. There are a few key commands you might find useful:
To lock the drawing to a circle:
Hold the shift key to restrict the ellipse tool to a 1:1 aspect ratio.
To make the initial point the center instead of a corner:
Holding the option key while drawing with the ellipse tool will place the initial click point at the center of the ellipse instead of in a corner.