You can only chat with people you have matched with. Once you do, you can send them unlimited messages on chat. The more interesting your messages, the higher the chances of you converting it into a conversation. So go ahead and start off on the right note. Tell them more about yourself.
Once you get a match, only then you can chat and send unlimited free messages to your match. For that, you need to tap on matchbox icon and select the user you want to chat with.