First off, I want to say thank you to all of you who commented on the last post. I am happy to see there are so many ladies interested in these little everyday things from times gone by. I was sure no one would be interested in my crazy history nerd musings; I am glad I was proven wrong. Thanks everyone!
OK, so we went through why housewives of the past used a dish tub for washing up, now what was their dish washing technique? The tools you need are few: dish towel and dish soap (recipe for hand and machine soap here). You can also use a washing tub if you have a large sink bowl, but you can also just fill your kitchen sink, seeing as most of us use the kitchen sink mainly for washing dishes and don't have to worry about dirt. The dish towel for washing can be a clean rag, an old shirt cut into squares, or a scrubby cloth like this or these. I love using a wash cloth for dishes over a sponge because you can just wash them when you are done and not worry of germs and so forth. (You can also reuse the cloth to wipe down counters, clean the tub, etc.) If you don't want to make your own dish soap, ladies of the past simply used soap flakes, like Ivory. (Ivory discontinued their flakes in the 70s, so you would have to grate your own.) Some companies still make soap flakes for dish washing, like this brand, but I haven't used this company's products. I use liquid dish soap and am a fan of Method dish soap.
So now that we got the tool options down, lets go to the actual process. Fill one side of your sink or a washing tub placed in your sink 1/4 full (to start) with the hottest water you can get from your faucet. Mix 1-2 tablespoons of dish detergent (if using soap flakes, follow the box directions). While tub/sink is filling, scrape all food from your dishes and pots and pans before soaking. Fill pots and pans with warm water and set them aside (don't put them in the soapy water bath). Immerse dishes into sink/tub bath.
There is an order to what you wash, so if you have a large amount of dishes, you may have to place your dishes in the water bath in sequence by washing "sets." Back in the day, most housewives did dishes after each meal, or at the minimum, once a day. With that upkeep, they probably could fit all that sessions washings into one tub/sink. You want to wash items in this order:
3) Plates, saucers, and bowls
4) Serving dishes
5) Cutlery, knives, and cooking utensils
7) Pots and pans
Ready for some actual washing? Rinse off any remaining food and use a scraper for any stuck-on food. Wash all items one-by-one, rubbing with the dishrag while they are immersed in the dishwater. Let the finished items sit stacked up in dish bath until you've finished that set of items (plastic, glasses, etc). When you've finished a wash set, turn on your faucet slowly and rinse the washed items. Let the rinse water go right into the dish bath. Put items into a drainer or a clean dish towel to dry.Clean each set of items using this method.By the time you are ready to wash you set-aside pots and pans, the dishwater will be near the top of the tub/sink from rinsing. To combat the extra grease of pots and pans squeeze a little extra dish soap on the dishrag. Use this water to wet the dish rag and wash pots and pans in the other side of your sink (if you have one) or use the counter. Do not immerse the pots in pans in the tub, unless you do not plan to reuse the water.
Reuse the dish water? Yeah, this may sound weird to some, but after you've finished washing all of your dishes, you can use the dishwater to wipe down your kitchen counters, cabinet tops, and the stove. The reasoning is that the water isn't really that dirty since the food was scraped and rinsed away and of the large amount of soap used for the bath. When you are all done, drain the tub/sink and wipe down your sink.
Resources: EHow "How to Wash Dishes the Old Fashioned Way."