There are two places on ZMZ to send messages - from the "Messages" page (accessible from the options at the top of the page), and from the "Messages" tab within every active project. These instructions apply to both.
Once you get to the message thread you're looking for, you'll see an area at the bottom with the words "Write your message...." Simply type or paste your message and press enter to send.
Users can only message other users who they're currently engaged in projects with.