Airport Extreme PPPoE auth and wireless
From your description you have a modem provided by your ISP and a separate access point or wireless router given by them that at the moment gives you Wi-Fi access to the internet.

You have to replace this access point or router with your Airport Extreme.
Open (or download, if you're on a Windows box) the Airport Utility app that will allow you to configure the Airport Extreme. Then follow the instructions provided at the Apple Support page:


  AirPort Utility 6.x: Connect to the Internet using PPPoE
  
  Some DSL and cable modem Internet service providers require you to use
  Point-to-Point Protocol over Ethernet (PPPoE) to connect to the
  Internet.
  
  If you’re using a DSL or cable modem, make sure it’s connected to the
  telephone or cable jack, and to your wireless device’s wide area
  network (WAN) port before setting up your base station.
  
  
  Open AirPort Utility, located in the Utilities folder in the Applications folder, select the device you want to set up, then click
  Edit. Enter the password if necessary.
  Click Internet, then choose PPPoE from the Connect Using pop-up menu.
  





  
  Enter the account name, password, and any other information your Internet service provider gave you. When you set up your base station
  or your AirPort Time Capsule to connect using PPPoE, the device
  receives an IP address from your ISP automatically, and uses DHCP and
  NAT to share that IP connection with computers on your wireless
  network.
  Choose Always On, Automatic, or Manual from the Connection pop-up menu. If you choose Always On, your wireless device stays connected to
  your modem and the Internet as long as the modem is turned on.
  
  
  If you choose Automatic or Manual from the Connection pop-up menu, you need to choose an increment, such as “10 minutes,” from the
  “Disconnect if idle” pop-up menu. If you don’t use an Internet app
  after the period of time has passed, you are disconnected from the
  Internet.
  If you choose Automatic, your wireless device connects to the modem, which connects to the Internet when you use an app that
  requires an Internet connection, such as an email, instant message, or
  web app.
  If you choose Manual, you need to connect the modem to the Internet when you use an app that requires an Internet connection.
  
  Choose an increment of time, such as 30 minutes, from the “Disconnect if idle” pop-up menu if you want to force the base station
  to disconnect from the Internet when it isn’t used for the specified
  amount of time.
  Click Update to reset the wireless device with the new settings. If your web browser reports a connection error when you access the
  Internet, wait until your computer is connected to the AirPort network
  and make sure the network is connected to the Internet.
  
  
  To check the connection, use the wireless connection status icon in
  the menu bar on a Mac, and the wireless network icon in the status
  tray on a Windows computer.


On the Wireless tab you want to select "Create a wireless network" and specify the security, SSID and password. You can check additional options but let's keep it simple.



On the Network tab you have to select "DHCP and NAT" on the Router Mode (it does not allow me to modify it, probably because I selected "Create a wireless network" on the Wireless tab).



Please check your settings and comment if this does not solve your question.