1. Turn on file sharing on the home computer, if you haven't already.
2. On your router, forward port 548 for AFP, 445 (i think) for SMB to your home machine's IP. Or if you have multiple machines, use a specific public port, say 549, and forward that to 548 internally to your home machines IP.
3. Get your external IP (internet IP) from your router and jot that down.
3a. Or setup a Dyndns address (use the widget to update your IP) and use that to connect.
5. Test the setup before you actually leave. You can test it at home, just go Finder--> Go --> Connect to Server (or command + K in Finder).
For SMB
If you used a different public port, be sure to use that and not the private port.