GIMP/Saving

This shows a typical image editing window in the GIMP (this is version 1.2, more recent versions will have a set of menus at the top of the image window)

Right-click, File, Save is used to save the image. A filetype can be selected (png, jpeg, etc.) from the dropdown list, but the default action is to use whatever extension was typed (specifying "image.jpg" causes it to save a JPEG file)

After the filename is specified, there is an additional dialog box specific to each filetype. For example, a JPEG image will ask you for the compression level, and it can be useful to adjust this until the image is a reasonable filesize.

Image formats Supported by GIMP
as of GIMP 2.2.13

Other less popular image format also supported by GIMP:

Other file formats that GIMP can only read, but not write:

GIF images
The Unisys patent has now expired and in recent versions of the GIMP you should be able to save compressed GIF images using GIMP.

If your version will not save GIF files and it is updated, you may want to update the corresponding image libraries for GIF.