Quick answer
You can use a “user override” to grant an individual extra time.

Full answer
Firstly, set up your quiz. Now…

1. From your course page, click on the Quiz activity.
2. Click on the “cog” icon on the right-hand side and select “User overrides”.
3. On the “User overrides” page, click “Add user override”.
4. Firstly, select the user for which you need to create the override (start to type in the box to filter the list). Click on the student entry in the list to select that student. Note that you need to do this for one user at a time. You can create group overrides too, but this requires students to be added to a group first.
5. Now select the elements you would like to override. Unless changed, the elements will inherit from settings of the current Quiz. There are several elements available for you to modify, including number of attempts, time limit (total time allowed) and start/end time. To allow a student to begin at the same time as everyone else, but to have extra time (the most common scenario), ensure you extend the end time and the total time (otherwise the original end time will override anything you put in the “time limit”).
6. Once you have modified the settings for the student, click on “Save” (or Save and enter another override if you want to set overrides for another student).
7. Having defined an override for one student, you may wish to set the same override conditions for another student too. To do this, from the main “User overrides” screen, click the “Duplicate” icon next to the user override that you wish to copy.