At least three option here

1. Join both the computers together using your home network. (If you have one)
2. Use a large capacity thumb drive.
3. Use an external USB/Firewire hard drive.
4. Email the files to yourself and download them on the second computer.
5. Use Dropbox on both computers.

4 and 5 require you to have an internet connection to both computers. If you have that, and both computers can access the internet at the same time, then you probably have a home network. If that is the case, then option #1is the best choice