How do you take the studs out your nose?

Properly done nostril piercings don't have backings on them (those with backings are not proper nostril piercings and were done with a piercing gun) they are of a screw design to prevent them from being snagged and pulled out by accident. You need to twist the nostril screw around till you can see the bottom of the screw portion inside your nostril, grasp the top of the nostril screw and gently pull down toward the edge of your nostril, then simply twist the screw until the jewellery comes out of the piercing. If you are still having issues see your local professional body piercer for assistance.