The quickest way to assign several tasks to a Team mate on Outplanr is through that Person filter on the left-hand menu.
Just select the Person's name on the People list, and pick the right project filter - "Your Projects" (meaning common projects), "All Projects" or pick a specific Project name.
Then all you need to do is create tasks under that Project name. All tasks will be automatically assigned to that person.
If you prefer to add tasks on a specific date, to a specific person, the best way is to do it on the Plan view. Here you can pick the person and the start date for the task. Any task added on this view will be automatically associated to that person and will have a set start date, all in one go.