To send messages in Core you must first be friends with the user. If you are not friends, then you will not be able to send a message to them.
To send a message, go to your friends list and locate the player's name. Once you have found the player you want to message, click their name. That opens a box with options and one of them is messages. Once you press that, it opens a private chat box with that player and you can type up your message. You cannot send messages from the player's profile, but only from your friends list. Once you have sent a message the player can respond.
Related: How to Add Friends in Core
Core also supports voice chat which can be both a general voice chat or a party chat. Additionally, once you have started a party, you have access to a party chat that all players in the party can see and respond too. There is also a general chat in which all players in game can see. You can cycle through different channels once in the voice chat with tab. Another form of communication is to walk up to the player and inspect them which will then give you access to quick emotes.