How do you set up a Virtual Proxy Network (VPN) with only one Linux computer?
The condition is that you can set one up yourself.
A VPN connection needs a starting point, usually a client, and an end point, the VPN server. Therefor setting up a VPN connection 'on a single system' is, I believe "pointless" would be the right term?
Is it technically possible? Yes.
Setup a VPN daemon on your Linux machine. Setup a VPN client on your Linux machine configured to connect to the servers IP, hostname or even localhost if you will (since it's on the same machine).
The most common choices are OpenVPN and PPTPd