This tutorial uses GIMP 2.6. It should work in later versions, but there may be differences with older versions.
Open the image you want to work with in the GIMP.
Activate the Ellipse Selection Tool, by pressing E. It's the second tool in the toolbox.
Click and drag inside the main image window to make a selection. After releasing the mouse button, you can further adjust the selection by clicking and dragging on the inside edges of the bounding box that surrounds the elliptical selection.