After getting to the eleventh mission of the game (the Cloaked of Silence) you will have your first chance to meet Quiet. Your mission will be defeating her in a duel which will happen in Aabe Shifap Ruins in Afghanistan. You may read about the details of this duel in our walkthrough however we would like to remind you that you may win also by taking down her entire health bar by with, for example, a sniper rifle or a rocket launcher or by taking down her entire endurance bar with, for example, a stunning weapon or by sending against her some supply drops.
After defeating Quiet you have to get close to her. DON'T KILL HER or you will be unable to recruit her. Better wait for Big Boss to hide his gun and lift her from the ground. Take Quiet to the helicopter which will take you to the ruins where you will be able to watch a long cutscene showing your return to Mother Base and putting Quiet in the prison.
Now you should focus on completing other missions. After the 14th mission (Lingua Franca) you will unlock a Side-Op titled 111 - Visit Quiet. Get to the Mother Base and head to the Medical Platform. Look for the stairs shown on the screenshots above. Go downstairs and listen to new conversations and watch new cutscenes as well. From now on Quiet will be your new buddy.
Information about Quiet and how to use her help
Quiet will be most useful as the sniper supporting you in the battle. She may eliminate your enemies from a distance and help you if you will be detected. She is not the best choice if you want to stay undetected since she needs some new, silenced weapons to really be useful in these situations. Quiet may also help you with the reconnaissance since she may mark your enemies on the map sometimes even better than D-Dog however she can't get wherever she wants. Because of that she can't detect the enemies who are hidden in the buildings.
Developing the relations with Quiet may begin even before she will join your team. When she will be taken to the prison you may visit her from time to time to bond with her. Beside that you may just use the basic way which is to give her orders and to use her special abilities during the missions. Fun fact is that you may actually bond with her by looking at her during your travels in the helicopter. The most important option which she will unlock through your bond is an access to the group of inventions which will allow you to provide her new weapons which will make her very useful.