I have a computer that is connected to a basic router.
How can I set up a VPN connection that will work over the internet?
Or what do I need to set up a VPN connection behind a router?
The computer has windows.
Most consumer routers have a PPTP (or VPN) passthrough mode that you can enable.
Other than that, most VPN clients shouldn't have much trouble connecting to a VPN service, unless your firewall is blocking those ports.