I am surprised that Roddy here is the only one who mentioned this.
When I do dishes by hand (which is rare since I hate doing dishes) the algorithm is:
fill anything really dirty with soapy water and set it beside the sink to soak.
fill sink with as hot as you can stand it water
wash glasses then cutlery then plates then relatively clean pots*
give the really dirty items a quick swipe and dump the water into the drain of the second sink
scrub and clean dirty items*
Note that I do not rinse things. A little soap never hurt anyone.
Aside: we have a rule that no dishes go in the sink. They either go in the dishwasher (if it is not currently running), in the spot on the counter where dishwasher safe items go (if it is currently running) or in the spot on the counter where hand wash items go. Dishes in the sink annoy the heck out of me. I use the sink all the time (to wash my hands, get a glass of water, rinse veggies when I am cooking) and reaching in to get damp dishes that have been sitting there squicks me out.
Every dish that needs it gets scraped, so all grease and food residue goes right into the garbage.
Dishes go into the dishpan; plates standing to the left side, bowls and mugs in the middle, flatware on the right/bottom.
Fill the dishpan with hot water with a squirt of dishwashing liquid. Start washing as the water starts running, so by the time the dishpan is full most of the plates are done. Plates, then bowls, then glasses and mugs, then flatware. Wash with the scrubby sponge, then put into the rack in the other side of the double sink. They go in that order because that’s the way they fit best into the rack. (The flatware goes into a separate holder.) Any casserole or glass baking dish comes next, and if the water is still good enough and the rack still has room, pans come last.
Air dry.
The whole washing process takes less than fifteen minutes, and the puttting away after they dry takes about three.
Generally speaking, I only hand wash what won’t fit in the dishwasher, either because it’s full, the item in question is awkwardly sized, or hand-wash only.
Generally speaking, it’s more of a size issue; we have a couple of cutting boards and stock pots that won’t fit in the dishwasher very well, so they don’t fit terrifically in the sink either.
The usual procedure is to soap them up with a very soapy sponge on the right side of the dishwasher, then rinse using the sprayer with lukewarm or cold water on the other side of the sink.
If I have a bunch of silverware, glasses or other small things that I’d usually put in the dishwasher, I load up the right side of the sink with warm/hot soapy water, then put the dishes in, and start scrubbing; as I scrub, I rinse on the left side with lukewarm water, and towel dry. At the end of the scrubbing, there’s nothing left in the soapy water.
I almost never fill the sink with hot water for soaking. I usually just wash the dishes with tepid-warm water and a soapy sponge, making sure I really rinse thoroughly.
I use the dishwasher for the bulk of the dishes these days, and clean pots/pans and such by hand.
Washing the dishes in greasy, dirty water and not rinsing them well enough is super gross.