Well you probably already have sshd setup on your desktop, I'm not 100% familiar with the way Fedora Core does this but I think starting it is something like `service sshd start` if it's not already running (which it also probably is).
All you'd need to do then would be to `scp` the files over, and I would suggest doing that from your laptop for simplicity's sake, but it's not necessary, you can do it from either machine.
Once you have ssh server (sshd) running on your desktop you can, from your laptop, simply type:
scp -r UmneyDurak@192.168.0.100:/home/UmneyDurak/files ~/
which will copy your files from your desktop to your local machine. You can optionally tar-bz2 or tar-gz your files on your desktop beforehand into one potentially slightly smaller file, but the -r flag will do the same as it does with cp or rm and recursively copy folders and files, so again, not strictly necessary to tar them.