Get a mirror that doubles as a sort of magnifier to view the area around your nose closely & carefully. You're looking for seams around the nose with which to gain leverage to gently pry off the nose to get better access to the nostrils within & beneath. Once the nose has been popped off your face, you can rinse both it and the exposed nostrils out with some warm water, which should get rid of the dry, compacted mucus.
You may want to take a soft, thin brush while you're at this for a more thorough clean. Once both the removed nose and exposed nostrils are cleared to your satisfaction, realign your nose with the seams you found at the start and gently squeeze & press your nose to reconnect it with your face. A light splash of warm water and scrub should help reseal the nose to your face and make the seams less noticeable.
Everyone know the the real method is to grab it between your pointer and middle knuckles like you’re knocking an arrow. Then give it a good yank, and if you do it to someone else, yell, “got your nose!”, as loud as you can.