Navigating to the message section of the patient's chart, you will see a list of all messages that have been sent to this patient, along with all messages sent from this patient chart.
When you click on any of the messages, you will see the contents. If you look at a message you sent to the patient you will be able to see all the replies (if this was enabled) and if they have read the message.
You will also be able to see any messages that were sent from the patient's chart to another party. This feature is further explained here: