By default, the router won't have a password. Also, it's name will be linksys in the airport menu like you see. Read through the manual for changing the name of your wireless network and to setup the password. Doing so involves opening your browser (Safari) and put in the URL
http://192.168.1.1 and that will take you to the admin page. It'll ask you for user name and password which is 'admin' for both. Consult the manual for changing that default password as hackers will know the default accounts settings too.
Once logged in, click on
Wireless in the page menu. This will take you to another page. From here you can set the name of the wireless network. Look for the text field labeled
Wireless Network Name (SSID). This is where you'll name your wireless network. You can pick whatever name you like. Go ahead and click the
Save Settings button after this so it takes effect.
Next, from the Wireless page, click on
Wireless Security on the menu. This will take you to where you can setup the password. Set the
Security Mode to
WPA2 Personal and then set the
WPA Algorithms to
AES. Next, for the
WPA Shared Key is the password for accessing your wireless network. Be sure to keep note of the key for future reference like when you have a relative visiting that wants to connect. Hit the
Save Settings buttons once again and you're setup and fairly secure. The manual has directions for further security if you're up for it, but this much is the minimal security you need to do.