Alas you didn't tell whether both systems you want to transfer files between are using the same operating system or whether one uses Windows and the other uses Linux.
Please include as much information as possible about what you are intending to do; Linux (Unix) is such a diverse operating system environment that there is always more than one way to do something...
Well, I found a program that does not need complex configuration, is very simple to use and can do what you asked for (transferring files between two systems).
It is called unison (homepage:
http://www.cis.upenn.edu/~bcpierce/unison/)
It says it is used to keep two directories (folders) on different machines in-sync, but this means in consequence that it has to be able to transfer files between them, doesn't it?
Also, it is available for both Windows and Linux.
Perhaps you can give it a try.
While this might be sufficient for now, for the long-term you really should have a look at Samba. There are countless of tutorials online on how to set it up easily.
http://www.howtoforge.com is a good place to visit.
For small home networks it is perhaps already properly configured in Fedora.
Your Gnome filemanager Nautilus has Samba access built-in, and you just have to point it to the right location (in the location bar, type "smb://NameOfTheComputerYouWantToAccess/NameOfTheShare")
cheers
fabian