Change of IP / Configure AirPort Extreme
The WAN (the outside of your router) connection in the router (your AirPort) should be set to static if your ISP provide the information about IP, gateway, subnet-mask and DNS. Some ISP assign static IP remotely so you don't have and can continue using DHCP. It's all about what they tell you to do.

Your local computers should not need to change anything as the router translate all traffic from them to be displayed online as your static IP.

When it comes to the different numbers and where they are suppose to go it should be clear in the information from the ISP.