Open an image.
Create a new layer.
Use the marquee tool to make an oval on the new layer.
Fill the oval with black.
Duplicate the original image and place it on top of the oval on the layers pallete (ie. the layers pallete should show the original, then a layer with the oval, then a dupe of the original on top)
Right click on the top layer in the layers pallete and choose "create clipping mask"
Turn off the eyeball to the bottom layer.
You can then drag the oval layer or the top photo around with the "drag" tool to get it exactly how you want it.
Go to layers and click "merge visible" and you will have an oval shaped photo on a clear background.
Save as a GIF preserving the tranparency, or any other method that preserves the transparency.