Some of the most geographically interesting and visually beautiful areas of California are the deserts, and the best way to experience the desert is to camp there. Many areas of BLM land require no camping permits for self-contained "dry" camping. Contained fires are allowed in many areas. Off-road vehicles are allowed on established trails and in some open areas, for more details see Off-road vehicles in California.
No matter what others have left behind, practice Leave No Trace - pack it in, pack it out. In fact, you're encouraged to clean up other people's messes if at all possible.
All supplies should be brought in if not for the mere fact that obtaining supplies in the region can often be pricey. Remember though, the desert can be a desolate and unforgiving land, always bring more than you think you will need. Campfire BBQ's and fresh fruit are certainly treats for which you will develop a new found appreciation for. And typically, as car camping is the desired approach, you can feel free to bring in almost all that you need.
Bell peppers, onions, zucchini, tomatoes (best prepared in a covered tin)
Corn on the Cob and either regular or sweet potatoes(wrapped in foil and placed on the edge of your fire)
A hearty soup
A nice touch to wind out a long day of exploring is to cook with your campfire.
Try to stick to an existing fire ring and modify it into a 'key hole' shape(kinda like a circle with a square attached). The whole idea is to have one part where you burn your logs and another attached section that you can push the hot coals that you will cook with into.
If in a rocky region make a circle with the larger rocks and with some shorter flatter stones make the cooking section. If need be, use some smaller stones to prop up the larger ones or fill gaps to make the structure stable.
If in a relatively moist soil environment(some seasons this is the case!) create the same shape but this time by digging it into the ground. An shovel is obviously best, but an ax can be handy for this and breaking down firewood also.
Place a grill over the square section and as the logs begin to burn down into coals, push them under the grill. If you don't have a grill handy, a simple foil pan can work fine as long as you don't get it too close to the coals.
An all steel kettle can even be placed over this portion of the fire ring to boil your water.
Beef jerky and the road also go well together as long hours on the journey need a bit of flavor. Notable is a small shack on US Highway 395 simply named 'Fresh Beef Jerky' in Olancha. Its $20 for 3 packs, but its fresh made and quite frankly the best jerky around. There's plenty of pickled vegetables and free samples also.
Bring plenty of water. A standard rule of thumb is 2 gallons (8 L) per person per day. Of course this can be partially substituted with fruit juices or gatorade, but make sure that you have more than you think you'll need, particularly if its your first time venturing in. Sodas DO NOT hydrate you!
You may also need water for an overheating radiator.