Just because you are camping out under the stars does not mean that you can forget basic hygiene.
Bathroom facilities must be well away from your camp area and use wipes to clean your hands afterwards.
As you make camp decide what facility will be located where and make everyone aware. Have a separate area for the washing of clothes, as well as cleaning up after meals.
Do not forget to pack washing up liquid and an antibacterial spray for washing down all the different surfaces. Keep all utensils and plates etc clean at all times.
Food hygiene requires careful vigilance, as obviously keeping things fresh is very difficult, no refrigeration to rely on here. Fresh meat and fish will not keep for very long so it is better avoided. There are many dried or canned foods that can be used and they will last invariably until opened.
If you want to have some fresh food then buy only enough for your next meal, do not attempt to store as it is too risky. The incidence of food poisoning during a camping trip is common but is actually easily avoided. Wash your hands before cooking just like you would do in your own home.
The biggest challenge is finding a source of fresh water. Obviously bottled water will be available in supermarkets but after that it will be hard to keep water cool. You may be lucky and find a source of freshwater, like a stream or lake, but always be wary of pollutants etc.