The assign dropdown is found from within the editing screen for a task. Click the large button that says "New Contact". When you do additional input fields will be exposed. Enter the persons name and email and click the "Add Contac to List" button to complete the addition process.
The new contact form has only two fields above the list. One for the persons name, the other for the persons email address. This is all the information we need to manage tasks. When you finish adding your contact's information click the "add" button. Your contact is now added to the list and automatically selected by default.