Here's a bit of a tutorial.
This picture of Arnold is a good choice to paste a head on because the background behind Ah-nald's head is a fairly uniform color and without a pattern.
This image of Telly is a good choice to replace Arnold's head because it has the same amount of focus, has a somewhat larger but similar size head, and has a stark, contrasting color behind it.
I load both into Photoshop (the technique will be the same for GIMP)
Since the Telly background is cooperative, I use the magic wand to select the black. . .it outlines his head fairly well. I invert the selection so it now selects his head and body rather than the black background
Checking out the Quick Mask Mode (there is a quick mask button in GIMP too) you can see the outline of his head is set. A couple of problem areas are the earpad on the eyeglass (it was too similar to black for the magic wand to pick it up automatically) and we have to mask out the suit.
If you use the paintbrush tool while Quick Mask Mode is on, what you are painting isn't a color but a mask. Masks define what you're selecting to edit. I "paint" out the suit, and paint in the earpad
This is the final mask outside of Quick Mask Mode, a good, tight selection around Telly's head:
I cut Telly's head, select into the Arnold picture, and paste it
Selecting the background, I use the eyedropper (paint selection) tool to pick up the color of the background near Arnold's head. I paint out his head liberally with the paintbrush.
I select Telly's head and move it into position. I had to shrink it a little bit. There are a couple of problem areas. First, there is a halo along Telly's jaw we have to get rid of. Secondly, I went a little hog wild with painting out Arnie's head and some neck is missing. Finally, Telly's head is a touch more yellowish than Arnold's body.
I use the polygonal selection tool to select along Telly's jaw a few pixels past the halo
And then delete it.
Now, I choose image->adjust hue, saturation, lightness to address the color issue. (I'm not sure where it is in GIMP, but it's in there). If there was a focus issue, I'd also adjust the blur. If one picture was more exposed than the other, I'd also adjust the saturation. We're lucky here and just need to make Telly a little more red.
Little changes here are better than bigger.
I use the polygonal selection tool again to draw a neck outline to keep a sharp edge to paint against. I use the eyedropper on Arnie's neck near where I have to fill in and use the paintbrush to paint it back in.
Now this looks pretty good, but there's one little thing left
Telly's eyeglasses are too dark on the one side, where they used to show through to a black background. I zoom in, use the polygonal selection tool and then paint in using the same color I used to paint out Arnie's head. I turn down the opacity, though, since his glasses are tinted and I want to keep that somewhat-darker illusion intact.
Once that's done, we're done. Flatten the image (combine all layers into one) and save it.