from a command prompt, type ipconfig /all (assuming windows). If your ip address looks like 10.something.something.something, or 172.25.something.something, or 192.168.something.something, then your are on a NAT network. Those IP addresses are non-routable and reserved for internal NAT networks.
You can get a simple map of your network using tracert, which shows you the number of hops from your machine to your destination. If you do something like "tracert google.com", and see more than a couple of hops, then you can sort of tell where your network ends and external networks begin. Everything on your network will share the first few octets of your IP address, and if you have a firewall and a router you will see them as hops in the output. From there, you could do additional probing to determine other things about the machines by using something like nmap or similar.