Desktop version
To delete the dialogue with a person, open the list of all your messages and click on the X in the top right corner next to the dialog that you want to delete. Please note that the dialogs are removed irrevocably and can't be restored.
Mobile version
To delete the dialogue with a person, open the list of all dialogs in the mobile version, select the desired dialogue, hold and swipe it to the left. You will have three options: star, flag and basket. Choose basket to have your conversation irrevocably deleted.