You can see the originals at the "great pics" link above. They look like they would be easy to paste together, but don't be fooled. Look at the picture on the left here to see what happens when you try.
As you can see, the geological features just don't line up. The horizon and background are especially bad. Not a big surprise, as pretty much every camera introduces some level of fish-eye into the picture, and distorts things near the edges of the frame. Because of this fisheye effect, no amount of naive scaling will make the features line up, since the differences in distance between them is not linear. To make things even begin to line up, you have to do a Perspective transform on one of the pictures. Luckily PShop has exactly that tool under Edit/Transform. You may also notice the horizon lines are not at the same angle. So I had to rotate one of the pictures 0.4 degrees. At this point things look better, and the features come pretty close to matching. Though one picture is now trapezoidal so the overall pasted together image looks like some weird speaker-shaped thing.
The next thing to notice is that the color between the two photos is all wrong. This in fact takes a lot of work to fix. I did at least three different stages of Hue/Saturation adjustment layers on the right hand picture, (tweaking the master colors, only the blues, only the reds, etc) and one on the left-hand picture. If you look carefully at the final picture, you'll see that I still didn't get it right, and shadows on the left are much bluer than shadows on the right.
But it still *looks* right to the human eye, thanks to the next trick I employed. Right about the center of the picture just above and slightly to the left of the white tip of the red mesa in the foreground, there's a small ramp or tongue coming off the dog-leg ridge out further in the canyon. That ridge doesn't actually exist in the real Grand Canyon. It's a trick to fool your visual cortex into thinking that it's just fine that the shadows on the left side of it are blue-tinted, but the ones to the right are brown-tinted. When the shadows touched each other, it was dead obvious. Put a little strip of lighter pixel inbeteen them, and suddenly all is hunky-dory.
Aside from those major things, there were also many minor alterations. Ever after color correction the sky colors still didn't match, so I copied chunks of sky and pasted them back in across the transition, setting the transparency a little lower each time. This leads to a reasonably smooth gradient that looks pretty close to normal. The same trick was used with small chunks of ground to bridge the annoyingly visible vertical line where the landscapes met. I used the Clone tool a lot to smoothly continue lines of light and shadow, and used the smudge tool a fair bit to even out the spots where I felt the transition was still a little too harsh.
I'm pretty happy with the final product. It isn't perfect, and there are a few things that are dead giveaways that it was PShop'd. Even so, I really like it from an aesthetic standpoint. It's just a neat picture. And I like that you don't have to buy an expensive panoramic cylinder camera to create wider shots like this.
The final image is 2540 x 880 pixels, and ~605k. Enjoy!