These how to Setup Wireless with Ubuntu instructions apply to Ubuntu 9.10, Karmic Koala and Lucid Lynx assuming the wireless card is detected. You can check this list of known working devices to verify if your wireless card is supported 
Ubuntu should automatically connect to wireless if the correct drivers are present. Click on the NetworkManager icon and click on the wireless network and you will see a prompt for the network key. Enter your key and then you should be connected. 
- Open Synaptic Package Manager
- Make sure the LiveCd is in CD drive
- Go to settings > Repositories > Ubuntu Software
- Check the installable from cd and close
- Search for "bcmwl-kernel-source"
- Mark for installation
- Install it
- Restart computer
If the liveCD is unavailable you may be able to install "bcmwl-kernel-source" with a wired connection.