1) Double-check that you are using and can access the 'net on your
local computer(s) using the Airport's DNS lookup (your DNS Server is
set to something like 10.0.1.1 in your Network System Preferences).
2) Launch Airport Utility
3) Select your Airport, and click the "Manual Setup" button.
4) Select the "Internet" toolbar icon at the top.
5) If you are using DHCP as your configuration, you can skip this
step, as restoring the settings if something goes wrong should be as
simple as clearing out the DNS Server(s) fields and restarting the
Airport - otherwise _write_down_the_DNS_Server(s)_fields'_addresses_
in case something goes awry.
6) Enter 8.8.8.8 and 8.8.4.4 in the DNS Server(s) fields.
7) Click the "Update" button in the lower-right-hand corner.
8) Wait for the Airport to restart. After it comes back online, surf a
lookup address as well as an IP address to make sure that the new
settings are working (e.g. http://www.google.com as well as http://18.62.1.6).
9) If it isn't working correctly, relaunch Airport Utility and either:
clear the DNS Server(s) fields if you are using DHCP as your IPv4
configuration, or replace the addresses that you wrote down if not.
Good Luck!