I read that some people use tilt shift lenses for panoramic photography, and being that I currently have access to the Canon TS-E 24mm f/3.5 L II Tilt-Shift Lens I wanted to give it a try. Do I just shift the lens the furthest each way? Do I have to take more then 3 shots to account for overlap?
Using camera movements for a panorama is a good idea, but using the shift ability of a tilt-shift lens is a little less than ideal.
Ideally, you'd want to make sure that the lens stays anchored in space, giving exactly the same point of view at all times, and simply move the sensor around in the lens's image circle by moving the camera body relative to the lens. That would mean that there is no parallax at all when stitching the images together. With the camera body mounted on a view camera as a "digital back", that's precisely what you'd do.
Unless I've been missing something glaringly obvious, though, it doesn't appear that the TS-E 24 has a mount available in front to the movement block, so keeping the lens anchored in space would be difficult unless you have something like a macro focusing rail. That would allow you to offset the camera by exactly the same amount as the shift offsets the lens.
The TS-E 24 II has ±12mm shift, so you should be able to get away with three shots (left, center, right) on an APS-C camera or two (left, right) on a full-frame. Since there will be parallax, though, you may have to take more images to get satisfactory stitching. Depending on the complexity of the subject field (how many stacked layers of depth there are), you may have to take more—5 to 7 with APS-C or 3 to 5 with full-frame.