If you're talking about this site, look up at the top bar at the envelope symbol right next to your username. When you have an unread message, it will change and show the number of unused messages you have. If you click on it, it will also show a preview of who sent the message, the header of the message, and a little snippet of the message.
Also, there will be an exclamation mark by it if a mod or admin sends you a message.
My MTS writing group,
The Story Board