Which model router?
What you need to do is to access the router by typing the router IP address into your browser. You can find the router (gateway) address by typing ipconfig into your command prompt window if you don't know the address. It is usually something like 192.168.x.1 where x = 0, 1, or 2.
Then you can go to the address reservation section of your router configuration pages (see your manual) and assign the computer a reserved dynamic address; or if your router doesn't support address reservation, set a static address for the computer that is in the network range but outside of the DHCP assignment range.