|"how hard is it to add to the new hard drive??"|
You'll obviously have to open both computer cases, remove the hard drive from the old computer, then install it in the new computer & copy whatever files you need to the new drive.
Would you keep the old drive in the new computer & use it for storage? Or would you put it back in the old computer again? If you're going to put it back again, it's an awfully lot of work to go thru. And there's always the risk of damaging something when fooling around inside. If you're not comfortable swapping the drives & wiring back & forth, just setup the old system again & copy the files out to the external.