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.
Just pick them, and wash your hands before and after. Then put your boogers in a trashcan. I always wrap a piece of toilet paper around my finger when I pick my nose.
If it's hard to get them by picking, I use pliers in front of a mirror and then put the boogers on a piece of tp which I then throw into the toilet or trash. (Remember that if you use pliers, you need to be careful so that you don't stab yourself with them. Also wash your pliers before & after.)
Once in the bathroom. Wash your face. The water in your eyes will drain to you nostrils and dislodge any boogers. It also stimulates mucous production in the rear area of the nasal cavity, which further lubes and facilitates cleaning your nose. Proceed to blow nose over the sink then dry your face. You'll have clean nasal cavities and a refreshed and cleaner appearance as a bonus.
You pick them, period.
If you had no means to pick (no hands for example) they would eventually fall on their own when the all the hairs attached to them finish falling.