How do I know if my message has been sent?

Go to your Outbox on the left panel. There you will see a list of messages you have sent out. To see a delivery report of the message you sent, click on View Report next to the message.

You can click on each option or toggle the drop down menu to see who the message was delivered to. If it has bounced, this means that the number cannot receive text messages from your short code or they may need to opt in by texting in your keyword.