Web:
If you want to mark a message as done in the web browser, click on the tick in the open message. So you can move the message to the DONE folder. 

 

App:
In the app you have two options to move a message to the DONE folder:

  1. Move the required message in the inbox to the right. A blue button "Done" appears. When you click this button, the message will be moved to "DONE". 
  2. Open the message and click on the tick above to mark the message as done.

After that you can find the messages marked as done in the "DONE" folder.