When someone you follow sends a broadcast message, it will be delivered to your inbox (the far left option on the bottom menu). Just click on the user in your inbox to view their available messages.
Once you are in the message viewer you can scroll left and right to view the other messages you have received from them. Just press the unlock button in the bottom right of the screen to open the message.
You also have a direct message inbox, which is the second from the left icon on the bottom tool bar which looks like a message bubble. Here you can view the messages that have been sent directly to you.