Mr Shakespeare said:
"... How do I transfer thee, let me count the ways....." or something similar?
I am assuming you simply want to keep some data and/or config files safe while you do the upgrade on one machine. I would suggest just burn the files you want off to a cd/dvd and return them after the upgrade.
If there are two (and only two) computers involved, pick yourself up a cat5 crossover cable for a couple of bucks and set them up as a simple peer to peer network. You then have a number of file transfer options available to you. Mind you a small USB stick costs next to nothing these days as well.
I suggest rsync (grsync frontend) is a better option than straight copy, but either will suffice.
When you do the upgrade ( to Elyssa I assume), and assuming you have your data backed up somewhere else, I suggest you do a clean install, use manual partitioning and create three partitions as part of the install; "/" for the os, "swap", and "/home". Return your data to the /home partition and thereafter you can change the os as much as you like without affecting your data files.