When adding tasks to a project in the 'Tasks' tab of the project overview, you can assign one or more users to each task:
When one or more users are assigned to a specific task, only they can enter time against that task. The task will not appear as an option in the dropdown of the Track view for unassigned users.
When no one is assigned to a task, all users assigned to the project can enter time against the task.
Users will be able to see the list of assigned tasks along with their descriptions in their Timesheet or Day Track view:
Timesheet view:
2. Day view:
They can simply start tracking time on any assigned task by clicking '+Add time log' for a task from the list.
*** Please note that by default, tasks can be marked as completed only by Administrators or Managers, but not by Normal members. If you wish to also allow Normal users to mark tasks as completed, check 'Allow normal users to complete tasks' in the Account settings > Tracking form.