focus on single-pot meals so only one pot is dirty. Eat out of the pot.
“deglaze” (add small amounts of water, broth, wine, etc) the hot pan to get as much flavor into your dish as possible1)
either clean ASAP (oatmeal and other stuff that dries on) or soak
Scrambled eggs are notoriously difficult to get off pans. Some techniques:
don't eat scrampled eggs consider poaching or hardboiling eggs to minimze cleanup
heat the pan, then add a bit of oil and allow to heat. Spread evenly, cook.
after cooking, scrape off what you can with a flat wooden implement, then put a small amount of water (doesn't have to be potable) back into the pan and bring to a boil. Simmer or allow to soak. Scrape again.