Not saying this is the best way, but it's the way I do it. I plug the left side of the sink, let the water run until it's hot, and fill the sink with hot water and a good squirt of Dawn Pure.
I scrape as much food as possible off the plates into a bowl that we call the deer bowl. We live in the country and are on a septic system so all scrap food goes outside for the deer or onto the compost pile. I stack the plates in the water, making sure that soapy water gets between each plate. I fill the sink with first the plates, then the silverware all together on one side, then bowls and glasses. I do not put extremely sharp knives in there. I fill the sink to the top and walk away for awhile to let everything soak.
Using a Dobie scouring pad with my left hand, I pick up a glass and lightly scrub around the inside and the rim, then, moving to the right side of the sink, I rinse the glass in hot running water. I place the glass on a drainer to the right of the sink. I take care not to run the water continuously, just enough to rinse, then turn off. I wash and rinse all the glasses in this manner, then the bowls and then the silverware, using the Dobie on each item. I run my fingernail along the tines of the forks to make sure there's no food residue left. Next, the plates.
Finally, when the sink is empty of these items, I stack pots and pans in the sink and allow them to soak for a short time and repeat, scrub, rinse, stack to drain. I polish the outside of the pots and pans right away to avoid water spots drying on them.