The home page of Classlist shows a list of the groups you are in. If there is new activity in a group there will be a blue number.
The notifications bell at the bottom of the app (or on the left on the computer) lists all your new notifications individually.
Creating a post to your class or group
To create a post to your class or group open the group and choose 'Write a post' at the top.
You could alternatively click on the pink 'Create' icon which hovers at the bottom right of the app screen.
The pink create icon is a shortcut to write a post, write a private message, create an event.