The base station must use an external DNS server, such as that provided by your ISP.
To change your DNS setting do the following:
- 

- Open AirPort Utility (in the Utilities folder). 

- Select your AirPort base station. 

- Click Edit. 

- Click the Internet tab. 

- Delete the manual IP addresses set for DNS Servers and IPv6 DNS Servers. 

- Click Update. 

The AirPort base station will now use the external DNS server, and devices on the Guest network should be able to connect to the Internet.