Gimp photo editing. How to replace a person in a picture (eyes closed, no smile) with another picture of them?

I am new to photo editing, so I am not sure if this is an advanced topic or not. I recently downloaded GNU Image Manipulation Program (GIMP). What I would like to do is be able to replace a person in a picture with another picture of the same person. My girlfriend and I went to a botanical garden and we took quite a few pictures of us (from a tripod and other people walking by that were kind enough to snap a couple of pictures of us). We have a bunch of pictures to work with, but the photography god wasn't smiling upon us when we were taking pictures. In the pictures where she looks good, I am grinning like a serial killer or loon. In the pictures where I look good, her eyes are closed or too open. There are some great pictures of us individually in the photos together, but no really good pictures of both of us together. What I would like to be able to do would be replace either me or her in the picture with a good shot from another picture. I would google it, but I am not sure what you call doing something like this. If anyone could give me a basic run down on how to do it or maybe direct me to an online tutorial or youtube tutorial, I would really appreciate it. Thanks.