device on network using same IP address

The protocol that assigns IP addresses automatically (and makes sure they're unique) is called DHCP. Enable the DHCP server on your base station, and set all the clients to get an address from it.

Launch AirPort Utility, select the base station, go into Manual Setup. Select the Internet page of the settings. Select the Internet Connnection tab, and from the Connection Sharing menu, choose "Distribute a range of IP addresses." That will cause the AEBS to act as a DHCP server on the local network.

The protocol that assigns IP addresses automatically (and makes sure they're unique) is called DHCP. Enable the DHCP server on your base station, and set all the clients to get an address from it.

That is too vague an answer to be practical.

For one, the likelihood is that the DHCP server is already enabled in the AirPort Extreme - or, at least there's already a DHCP server running on the network. If it's already running then 'enabling it' is not going to help. If it's not already running then you just enabled a second DHCP server in the network which is going to cause even more problems.

Besides, you cannot easily "set all the clients to get an address from it". DHCP uses a broadcast protocol to find DHCP servers and, generally, whichever server responds first is the one the client will use. There's no client-side way to tell any given device which DHCP server to use.

Besides, as described, it's not even clear that the IP address is even in use by another DHCP-based client. It could be some other device on the network (printer, maybe?, Blu-Ray player? PS3? X-Box? or even some rogue client) that's configured with a static address.

The actual solution to this problem requires some troubleshooting. You'll need to start off with the base station - it will give you a log of the connected clients listed by MAC address and assigned IP address. Cross reference this list with the known devices (Mac, iPad, and iPhone) and you may find the rogue device. Once you have the MAC address you can start to trace the device on your network.

Click the icon labeled Internet.

You say you have a Mac laptop that's working properly on the same network. Please open the Network preference pane on that laptop, select the AirPort connection, and click on the "Advanced..." button. You now see a tabbed sheet. Select the "TCP/IP" tab. There's a menu labeled "Configure IPv4:" What is selected in that menu? Below that are some settings: IP address, subnet mask, router, DHCP client ID. What are those settings? What are the corresponding settings on the problem Mac?

That all looks correct. You have two other devices on the network (that you know of.) Please check their network settings. They should both be getting an address using DHCP, and their settings should be the same, except for their IP address which should be different. If that's the case, then please restart your AEBS and try again to connect with the problem Mac.

If it does, it may be that someone has cracked your network.

You should use WPA 2 Personal as the encryption standard, and choose a password with about 20 characters, random letters and numbers.