|The interface that will be connecting to the internet should be easy enough assuming you have an SOHO router between you and the internet. If you do, DHCP is likely enabled on the router so all you should need to do with the interface on your computer is ensure it's set to "get TCP/IP settings automatically (DHCP)"|
As to the other network the best thing would be to set the IP address on that interface statically. You would of course want one in the same subnet but I would not configure a "Default Gateway" address for that NIC as it won't need it and this would avoid having your PC attempt to send internet traffic that way.
I will warn you up front that Windows has some issues multiple NIC's so you'll want to be careful. I would recommend using one private IP range on one interface, and a different one on the other.
So let's say by default your router is using 192.168.1.0/24, I would use 10.0.0.0/24 on the private LAN.
Traffic can't flow between the two networks on your computer. In order for one network to access the other, you'd have to manually setup static routes on your PC.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.