You just need to make sure port forwarding is set up correctly (put simply, so that the router knows which PC to send incoming game data to). To do this you'll need to know the ports the game uses to host and add these to your router's configuration along with the host PC's IP, usually via http or telnet depending on the router.
Before you go ahead with all that, you can try setting the host up as the default machine or DMZ. Assuming your router isnt already forwarding to other PCs, setting the host up as the default recipient of incoming data will essentially be the same as a direct connection to the internet, but it's the most clumsy and least secure way of doing things, effectively eliminating any security benefits of a router. DMZ options are normally alongside port forwarding options in the router configuration.
Have a look here
for a description of the principles and technologies, and the differences between forwarding and using a DMZ.
In either case, you'll almost certainly need your host PC to be using a static IP rather than a dynamic via DHCP, which you can do in TCP/IP properties. The static IP you set should be outside of the range of the ones the DHCP server uses (usually that means the last number must be >32, ie 192.168.0.40).
If you need any of this in any more detail, tell us what router you have, it's LAN IP if possible and the game you're trying to get working.