There are several types of nose rings, each with its own set of pros and cons. Hook nose studs, also known as nose screws or corkscrews, aren't likely to fall out, and come in a variety of metals and decorations. However, they can be difficult to insert, and may damage the septum if the nose gets hit.
Wash your hands and face. Look at your piercing. If it is red, inflamed, or has any signs of pus, do not try to change your jewelry. You risk irritating your piercing, which could cause or worsen infection. If you can comfortably wiggle your current nose ring, you will have better luck inserting the hook nose stud.
Clean your hook nose stud with rubbing alcohol and allow it to dry. Hold the hook nose stud up to your nostril and check to make sure it is the right size--if it is too big, it will not fit comfortably inside the nose, and could cause damage to your septum. Also check the gauge, or the width, of the post. If it is bigger than your current piercing, do not insert it.
Remove your current nose ring. It can be difficult to remove fixed bead rings, barbells and pins with bones. Do not risk damaging your nose; ask for help from a friend, or go to your piercer to have it removed.
Holding the top of the hook nose stud (the decorative part), line up the end with your piercing so the curved portion is arching away from your nostril. The part you are holding should be facing down, pointing towards the floor. Take a deep breath, and as you exhale, insert the hook and twist it until just the straight portion is showing.
With the tip of your finger, push the hook nose stud up into your nose until it is in a comfortable position. Adjust as needed.
Tips
Wait at least three months after having your nose pierced to change the jewelry. If you don't let it heal completely, it will be painful and even impossible to put a hook nose stud in.