Once you have assigned a to-do to a student, the to-do will be listed on the To-Dos tab of the student's account. Students will not automatically be notified when a to-do is assigned to them; however, you may create an alert so that the student receives an email reminder in advance of the task due date.
For more information on adding a To-Do alert, see: How do I add an alert for student To-Dos?
Also see this related article: How do students view and update To-Dos?
Should you need to inform a student immediately about a new to-do item, posting a message to the Conversation would be the best option for reaching them quickly.