There are several options:
1. E-mail the files. If they're not too big, just send them via e-mail.
2. FTP. Your Mac can be set up as an FTP server (make sure the OS X firewall is on, and be careful with directory permissions) that the remote computer can access.
3. iDisk. If you or other other person are a member of .mac, you can share files via your iDisk.
4. Third party services. There are other web-based providers of online storage that you could use. Not sure of the cost and security there.