How can I merge an image scanned in parts into one complete whole?

If you really want to do this manually, I think you could create an image large enough to hold the end-product, then paste the pieces in (probably each in their own layer) and align by hand. When you're done sliding layers around, you could then merge back into a single layer.

Alternatively, you could re-scan with a little overlap across images and use something like Hugin to stitch them back together again. This might end up being easier and more reliable in the long run.