Does anyone know how to do this? I've got a mod I started working on several years back and made a lot of progress on but never released it. I am wondering how difficult it would be to transfer the data from my old computer to my current machine in order to continue work on it.

Just grab your .esp and any other files that are associated with it (for example, if you've implemented custom meshes, textures, voices, etc.) from \Steamapps\Common\Skyrim\Data. Then, after you install Steam and Skyrim on your new computer, just drop the .esp and other files back into that folder on the new machine.