There is no push to talk function for the microphone, it is automatic. As long as you have a microphone and it is set as your recording device in your sound properties (this is found in the Windows Control Panel), then it should work automatically. If the other player does not have a microphone, I do not know if they will be able to hear you (ie. if it auto mutes you on their end). If you decide you no longer want to hear someone, you have to mute them from the lobby. Unfortunately, there is no way to do this in-game so you would need to rehost in order to mute the other player (a little odd I know).
I can confirm that the game has built-in voice chat as a friend and I playing coop on PC had to mute each other from the game lobby. We have a Ventrilo server that we use instead and the voice-activated transmit tends to drive us a little insane.
