Inside of a student's submission, the due date at the top of the page has an Extend button next to it: 

Clicking Extend will bring up the following dialog:

From the Project page itself, you can grant extensions using the bulk functionality. If you click the checkbox next to 1 or more students, the buttons on the right will enable for bulk actions:

Clicking Grant Extension while having 1 or more students selected will open the same dialog as above, but all students you have selected will be granted extensions (since we've selected 2 students above, the title of the modal will reflect granting to 2 students):

Assignment extensions can only be granted via the bulk actions similar to the ones shown above:

If you grant extensions on quizzes with Time Limits, more options appear to control the timer for the students.

You can change the time limit while a student is already in progress to extend the students timer. If you changed the time limit from 30, to 60 minutes, students will be granted an additional 30 minutes to the timer that is already ticking down. Students will need to refresh their assignment to see the updated timer. 

If you check the reset time limit option, the student's timer will be deactivated until the next time they access the assignment, and then it will start immediately upon accessing the assignment with the time limit specified in the extension.