The user who will be listening in needs to have the following permission set in 3CX admin:

Next, the user listening in should have the web client installed on their computer, and a headset hooked up.

Open the 3cx windows application and login with your extension

Click the Panel button on the left hand bar:

This will bring up the current switchboard of all currently active calls. Right click the call you want to listen in on and choose listen.

Your headset will start ringing and a 'bardge in call' will show up. You might need to change windows to the 3cx dialer to see this. Click the green pick up button to begin listening in. There doesn't seem to be any difference between choosing 'Listen' and 'Barge in', they seem to both do a 'Barge In' action.

Since you are just listening, it's probably a good idea to mute your headset.

Click the hang up button to stop listening in.