What files and how many files are we talking about here? If just stuff in "MyDocs" and such, and you don't have much there, if you have any external storage device, you could just use that in between without messing with any sort of networking.
If you have both on a home network (if you have a router ... if you have "wireless internet"),then you can setup a Windows Network... or simply put both machines on the same workgroup name, make sure one of them as sharing enabled for the folder(s) you want to share... if you're using Vista or 7 on the shared computer, also turn on password protected sharing (and put a password on your account if you don't already have one)... procede to grab files from other machine's desktop....
Well, the external storage will be the easiest any way you go, in my opinion. If you want to buy one of such, get a flash drive large enough to hold all the files... or else make a couple "trips" between. Flash/thumb drives are super duper simple to use.
Another option would be an external hard drive, cheaper for the amount of storage than a flash drive, but not quite as easy... though still super easy... you can connect via USB, eSATA, ethernet, firewire, whatever, just as long as that drive supports the connection type. My personal favorite is a combo USB/eSata... USB3 will be probably the best within another year or two.. just gotta get more market saturation for that one to be viable....
Anyway, if you use external storage, then you could also use the same external storage later as a backup of your originals.