One of the most important principles in outdoor cooking is keep it cool. Make sure that all your refrigerated ingredients are kept cold enough to be food safe for the length of the trip.
Buy yourself a reasonably new cooler. In fact, consider buying two. (More on that in a second.) Plastics technology has changed over the last decade or so, so older coolers do not retain cold nearly as long as the ones on the market today.
That said, the way you pack and use your cooler is just as important as the cooler itself. Use plenty of ice, especially for longer trips. Don't drain the water from the cooler as the ice melts. Water with ice is actually cooler than ice alone. Limit the number of times you go into the cooler. The more its open, the more the ice will melt.
Keep the common ingredients in one cooler and the frozen stuff in the other. Coolers work best when they are kept closed. If you restrict the number of times you open the cooler with the frozen food, you increase its ability to keep things cold.
If you are making dishes that need to be chilled before you eat, reserve a cooler for storage of those dishes. This does not have to be a large cooler, just one that has plenty of ice.
Start dishwater heating when you start preparing the meal. Heat the water in a large pan with a lid. The lid will keep the heat in and help the water to heat faster. If at all possible, heat your water on a propane stove rather than a charcoal or wood fire. It is better for the environment.
Scrape all dishes, pots, etc. before putting them in your dishwaster. Use a rubber spatula to get as much off your dishes as you can. This will increase the amount of time your water stays clean enough to use.
Set up a three dish pan cleaning station. The first pan gets hot soapy water. The hotter this water, the better the greasy dishes will come clean. The second pan gets warm to hot rinse water. Try to keep it free of suds so that you can use it longer. The third pan gets cool water and a disinfecting ingredient such as bleach. This eliminates any germs that were missed by the water not being hot enough. Air dry your dishes to eliminate the most germs - towels carry germs like you wouldn't believe!
As the wash water gets dirty, dump it through a strainer or a piece of cheesecloth to remove the solid waste. Throw away the waste and dump the water away from any campsite or trail. If you are camping where there are large animals, do not dispose of your water near your campsite.
I recommend doing the clean up of your cooking dishes while the food is cooking when possible. This saves overall cleanup time and gives campers something to do while waiting for the food to finish cooking.