In the firewall, you may forward port 80 (ie, HTTP) to the new web server. The web.config in the new website, the connection string must point to the IP address of the SQL server. If the web server is in the same network domain (ie, the ActiveDirectory) of SQL server, then, you can use the "integrated authentication". Else you have to change the SQL server authentication mode to "Mixed mode" and set the "user ID" & "pwd" in the "connection string" in web.config.
Hope it helps.
