You can only send a message to a user who follows you. This is to stop spam, scam and imposter attempts and general unwanted communication.
To message a user, go to their profile and click the envelope button in their profile info.
Once you have sent a message, you can always go back to Messenger and the conversation will still be there to continue.
You can also delete entire conversations, from within the messenger.
You can send images, GIFs and emojis in messages. You can also send links however they will not display as previews within messages.
To stop someone from sending you messages, you can unfollow them and also block them.