In this high desert, it is very easy to avoid the glare of human civilization. Just walk a few feet away from any road or camp, and you are in total darkness. Also, the skies are clear most nights of the year due to the low rainfall.
Tip: To get the best view of the heavens, try to avoid the bright moon spoiling your view. Check the moon phase calendar here https://www.timeanddate.com/moon/usa/los-angeles
For first time stargazers, I recommend visiting the "Sky is the Limit Observatory," located just before the north park entrance and Twentynine Palms.
Every Saturday, a large group of like-minded people gathers to enjoy the heavenly displays.
Many volunteers bring their large telescopes and allow people to view the Planets and Star Clusters.
Tip: When walking in the dark, use flashlights with red filters. Regular flashlights create a lot of light pollution and spoil the view for everyone.
You don't need a telescope to enjoy the show. Use your naked eye or binoculars to see many stars, constellations, the Milky Way, and a few shooting stars.
If you happen to be camping at Joshua Tree, then all you have to do is walk a few steps away from camper lights, where you will be plunged into total darkness.
Tip: It can get really cold at night in the high desert. Dress in layers and bring extra blankets.
As you drive around the park, you will notice those pullouts or small parking spots. Many of them are next to popular points of interest like Cap Rock, Jumbo Rocks, and Skull Rock. Wherever you park, walk a few feet away from the vehicles to enjoy a great sky view.
How to watch the stars
During my first stargazing visit, I wasn't fully prepared. I was trying to view the sky while standing up. I did enjoy some of the views, but before long, my neck started to hurt from trying to lookup. I also got very cold, even while wearing a jacket.
My advice is to bring a sleeping bag or thick blankest to lay on the ground. Lay down and cover up to enjoy an amazing view above.