Once you have unlocked Quiet, just start bringing her out on missions and Side Ops. In the buddy menu in the Missions tab, you can tell her to move to different Scout and Attack positions. With Scout, she can survey outposts and bases for you beforehand, pointing out some enemies and items of interest. With Attack, you choose a position for her to wait, and by holding
and choosing Fire, she'll shoot the enemy you're currently pointing at with your reticle if it's possible for her to do so from her position.
I recommend bringing her with you wherever you go. If you tend to go for a stealthy, no-kill approach, start by just using her to Scout out areas for you. Eventually, you can develop new snipers for her as your bond increases that tranq instead of kill and that have suppressors. The more you Scout and Attack with her, the faster your bond will increase.
NOTE: At time of writing this, taking her with you on missions 29 and 42 can result in a game breaking bug, so be sure not do that.