After logging into Typetalk, open the topic you want to read by clicking on it at the left sidebar menu. The topic messages will be displayed on the right.
If you have unread messages on a topic, you will see the number of unread messages displayed next to the topic name. When you open an unread topic, it will show the previous unread messages (up to 100 messages) and you can scroll down to see the latest posts.
If you are a member of more than one organization, you can check the messages in the different organizations by switching to another organization on the global navigation.