You would need to configure the AirPort to act as a router.....DHCP and NAT enabled....on a different subnet.
If you have not changed the DHCP range that your "main" network is using, all devices are receiving a 10.0.1.x IP addresses.
So, you would configure the "new" AirPort to use a different DHCP range.....say 10.0.2.x.
This will also create a Double NAT error intitially, which you can click to "ignore" and the indicator light will be green.
Clients on this network will have Internet access, but they not be able to "see" clients or devices on your "main" network, and vice versa. If you want the "guests" to be able to print, you will need to designate a printer for this network.
Post back if you need some help with this. Hopefully, you are using OS X 10.6.8 as your profile indicates, since this is difficult to do using Lion or Mountain Lion, and pretty straightforward using Snow Leopard or any of the 5.x versions of AirPort Utility.