This camping area is at the end of dirt road Route 21S69, there is a sign for Dome Rock. It's very close to Ponderosa, a small town(?) with a general store and lodges, so that makes it super convenient if you need to buy some standard supplies.
At the end of the dirt road there is a parking area. You can camping anywhere in this area, no fee. Just make sure to apply for a fire permit ahead of time. There are NO facilities at this campground - no bathrooms or trash even. That said, it is a beautiful area, especially if you want to rock climb or hike with great views, including The Needles. Rock climbing info for the area can be found here.
Keep in mind that this location is at ~7,000ft elevation, so the temperatures will be cooler here, and you should plan accordingly.