I think you would either need Internet IP addresses for ALL your devices OR you could set up a router to go between the internet and the LAN.
If your ISP only gave you one Internet IP address, and you have more than one device, then you have to use a router. The WAN port of the router would have the Internet IP Address assigned by your ISP, and all the internal devices could have private IP addresses in the 172.16.0.0 range.
All your computers inside you LAN would use the internal DNS server for their lookups. You would set-up the DNS server to forward any requests that are not in its database (such as yahoo.com) to your ISP's DNS servers.
[EDIT: Fixed Typo that changed meaning!
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Edited by wistex