To complete a task, open the Tasks Popup:
Check the box next to the task you wan to complete:
You can add an optional note if desired.
When you're done, choose Complete to mark the task as complete.
Completing other users' tasks
Depending on app settings, you can also complete tasks assigned to other users.
Just hover over the profile picture next to a task, and it will be replaced by the checkbox that you can click to complete the task.
Notifications and reporting
Depending on App configuration (see below) anyone assigned to the task, or watching the page will receive notifications to let them know of the changes.
Details of the changes will also be stored in the Activity Report - Content.