H1Z1 currently has only two ways of in-game communication, through VoIP or through emotes.
There are three kinds of VoIP channels: proximity chat, group chat, and radio chat. With proximity chat, everyone in a radius around the player can hear them talk, including zombies. With group chat, only people who the player has grouped up with can hear them talk. With radio chat, everyone that is on the same channel as the player can hear them talk.
Players will start with a standard set of emotes, but they can purchase additional emotes off the Steam Marketplace, or by opening a crate.