How do people put these images together? I take it it's more complicated than just opening all the images in Photoshop and arranging them so they line up.

that only happens if you're VERY VERY VERY VERY lucky... (a 1 in 1000000000000000000000000000000000000000000000000000 chance or something like that)
usually you find yourself having to transform (stretch/shrink) and rotate the pieces so they line up... getting it right can be time consuming... and frustrating....