I have 2 XBee Series 1 modules. Both are connected to Arduino Unos through the Arduino Wireless Shield. I am able to configure them and establish a serial connection while they are both connected to a computer. I am also able to send/receive messages through the console log.
I want to be able to wirelessly communicate without any of the systems being connected to the computer. I wish to have a button on one end, be able to press it, send that information to XBee A, which will send that to XBee B, which will turn on an LED at that end.
When you have them connected to a computer, do you mean that you are sending messages from your computer directly to the Xbee module without really using the Arduino microcontroller?
The first thing we would recommend would be to program one Arduino to act like a echo device: any Xbee message that it receives is automatically sent back. You can then use the other Arduino to verify if this is working properly. Then you can change the first one to turn on a LED based on the messages that it receives. Once you get that working, replace the code with code that will send messages based on a button press.
Finally when you get that done, you can put the first code (LED) on the other Arduino and see if the button messages sent by the other is received properly.
Hope this helps,