Unlike most Deskpro items, you can’t open a task in the content pane. (The only exception is if you have linked the task to a ticket, in which case it is shown in the ticket’s Tasks tab).
Everything you need to do with tasks can be done in the list pane.
At the top of the list pane, you can choose to sort by Date (most overdue at top, shown here), Assigned agent or Creator.
You can re-assign (delegate) a task by clicking the assigned agent or team, and selecting a new one from the pull-down menu.
To mark a task completed, just use the checkbox to the left.
Double-click on the title of a task to edit it.