There’s a little bit of neon in the air we breathe, so yes, our atmosphere contains neon.
You can extract it by using a process called adsorption. That involves superchilling the air at temperatures below 411 °F so it becomes a liquid. When you run the super cold liquid over charcoal, the neon molecules stick to the charcoal.
By raising the temperature, you can “boil off” and capture the neon. Unfortunately, there’s not that much neon in the air.
Manufacturers end up having to process 88,000 pounds of liquefied air to get one pound of neon.