We're currently using the new Mumble beta, version 1.2.0. You must have that version to connect. The below guide is for 1.1.8 and is significantly outdated.
Mumble is an open-source VOIP program that allows people to connect to a server and communicate with a microphone or other input device. It is comparable to other popular programs like Ventrilo and Teamspeak.
The main difference is that it's open source and best of all - free.
Once you have it installed, start it up from the desktop or the start menu.
You should get a menu like this. Follow the instructions in the screenshots to properly setup Mumble with the optimal settings.
You can make your Push-to-talk bind here so you press a key instead of the computer picking up your voice automatically. If you do this then you also have to enable Push-to-talk mode in the Audio Input's Transmission menu.