From here, you can start timer to track time and post time. Hours added in my hours are added only to the user who post the time for the task not to the Assignee.
To Track Time
Click Start icon for the task you are going to work on to track time.
To Post Time
You can also post time directly by clicking in the respective cell. Click the respective cell (selected task and its date). Provide the start and end time for the task and click save.