set your local host to the gateway (often a router) which connects to the outside network. If you are going outside to the internet ensure your dns settings are correct as well. Ensure your ip is on the same network as the lan interface on the router you point to. Check the subnet mask for continuity.
Whatever device is natting will pass you through (barring filters or rules on your ip or traffic type) and you are through to the other network.
If this is not what you are looking for post more info on your exact setup.