I'm often restoring maps (cut into 8, 9, 16 or more pieces) or torn photos and the like. They are scanned and then arranged in Photoshop. So I often have individual fragments that are already the right size but that have to be rotated and moved in the right place. As they don't overlap, auto-align layers is no help in this case.
I mainly use the rulers and guides to measure correct distances. The rotating part is the most difficult. It's a great thing that you can choose the point around which a fragment rotates because this way you can pin down an area you already know to be where it belongs while trying to find the right angle for the rest of the fragment, but still, it's tedious.
Are there more instruments that are regularly used for this kind of work that I just don't know about? Eager to learn new tricks.
I've successfully used Photomerge to automatically rotate and fit map pieces. However, for this to be successful, it is important to have overlap. The more overlap the more accurate the Photomerge.