I did this to transfer an OpenSuSE (Leap 42.1) system but should basically work for others. Partly going off the instructions here but deliberately not modifying the drives' uuid because I disagree with that approach (you might want to continue using the old drive for something else for one thing).
Boot into rescue system/live cd with current/old disk and new one both in the system. I create a directory for the old system and mount whatever partition looks like the right one to it.
mkdir old mount /dev/sdc2 old