Simply install SDC on the new machine, log in with your account, and download again exactly the same way as you did before. You don't need to do anything special at all.

You can find your saves and ship designs in My Documents\My Games\GalCiv2 if you want to copy those over as well (though you should delete the prefs.ini file since that could cause issues on a different computer from the one it was made on).

If you have a burner on your existing computer, or have a 1gb or larger USB thumbdrive, you can simply right click on GC2 in SDC and choose Archive Application->Selected Application to save yourself redownloading. If you only have a CD writer, say no when it asks you if you want to archive the extra modules as well, and archive each of them separately so you can split the files across two discs easily. Then just grab the .sdc files in C:\Program Files\Stardock\Stardock Central\BACKUP and copy them off and take them to the new machine. On the new machine, install SDC then just double-click each of those .sdc files in windows explorer to install them (do GC2 itself first, then the modules).