While the Moodle Support team can provide instructions to faculty on how to set up the Safe Exam Browser, the final responsibility of making sure that everything has been done properly (including the installation on the student's side) rests upon the instructors themselves.
The video below is an overview of the SEB in Moodle--while it is based on a previous version (3.9), it is still valid.
On a Moodle quiz, instructors can activate the SEB by clicking the dedicate tab in the quiz Settings menu. The simplest--and recommended--option is the manual configuration (Yes -- configure manually), keeping the default settings, which are:
Once the settings are in place, instructors can also download the SEB themselves (from the official page) and run a preview of the quiz to have an idea of what it looks like.
A good practice for instructors is to set a simulation test to be run in class to make sure that all students can access the quiz, after having downloaded and installed the SEB.
Once the instructor has set the SEB for their quiz, students can download and install SEB from the landing page of the quiz itself, by clicking the Download Safe Exam Browser button:
They will be redirected to the official page where they will choose the correct version, based on their device. As mentioned above, it is good practice for the instructor to set a simulation quiz to be taken in class, to make sure that everything is working for the actual test.
After having downloaded, installed, and tested the SEB, students will be able to take the exam by clicking the Launch Safe Exam Browser button on the quiz's landing page.