Mapping

It would probably be useful to use a VJ-ing/ mapping software and calibrate based on their internal tools. Otherwise it could be as trivial as feeding a bunch of grids into the projector and measuring the deviations/ adjust the output until everything lines up. Hard to be more specific without knowing all the details. Generally, though, this isn't anything to be too scientific about. Even today it's more trial & error and usually the problem isn't the content, but the physical setup of the projectors and lenses. 3D planning can help, but it's not essential.

Mylenium

There are two options. The easiest would be to take a photo of the cyclorama from the projector's position with the lens as close as possible to the projector's lens. You can then use Corner Pin to crop the photo to the corners of the cyclorama and fit the cropped image to the frame size of the comp. You now have a starting point. Pre-compose that layer, moving all attributes, then use tools like Mesh Warp to distort the checkerboard until it fills the frame. That should give you a starting point for creating a checkerboard that will match the real one on the cyc when projected. This works because perspective is determined by camera position, not focal length. As long as the camera and projector lenses have very little distortion, you should be able to line up the patterns on the wall.

The other option would be to create an accurate 3D model of the Cyclorama, including the projector's position, and then use that as a guide for your animated graphics. This approach is a lot more work.