Cleaning with water

Well, you know, water is pretty good.

Maybe you already covered this in the book.

For both laundry and dishes, water is the main cleaning agent.
Boiling water is especially good; for some things, it's better than soap.

Rinsing with boiling water is called "scalding," it gets most gunk off, and kills a lot of germs in the process.
I use this on most kinds of heat-safe dishes, from wooden spoons to glassware to the sink itself.

Boiling for about three minutes (some sources say 10) kills germs in sponges and dishrags.  It eliminates most of the nasty odors, although it doesn't entirely clear out the gunk the germs were feeding on.
So I will either do several boiling rinses if I have time / limited other options (like an office breakroom); or I will boil a batch once, then wash the sludge out in my tiny washing machine (the advantage being, after boiling, it doesn't stink up the washer, and I don't have any reason to use bleach-type stuff on the washer afterwards.)  
I do use a biodegradable eco-detergent for routine washing; but some of our friends use soap nuts in the laundry washer.  I would not call them "edible" for humans, but they're pretty bio-compatible.  

For pot and pans that get heated above boiling point, like cast iron, they tend to self-sterilize with each use. I will leave a coating of oil or butter on there, and I don't mind if it's the same oil I used to cook pancakes.  (If your oil is going rancid between cooking, you could make the case that you own too many pots, or don't cook often enough.  In that case, wipe off the old oil, leaving a very thin coating.

For sticky foods in cast iron, like gravy, I like to store or eat as much of it as practical; wiping out with bread while it's still fresh and tasty saves on paper towels or washrags.  
Then rinse with boiling water, scraping any stuck-on bits with a wooden scraper.  Avoiding soap on cast iron is part of preserving its non-stick cooking surface.

Avoiding mess is another good tactic, where edibles can be used.  Think "edible dishes" - such as bread trenchers, chowder or chili in a bread bowl, tortilla-lined baskets, or good ol' buns or sandwiches - is another trick for reducing the amount of dishes to begin with.  Lettuce or cabbage leaves, for the gluten-wary (most of us really don't need that much bread in our diet).  
Leafy liners can minimize the cleanup from serving meat and seafood, or free yourself to experiment with porous serving ware such as wooden bowls or unglazed / hand-glazed pottery.

The alternative, scrubbing with abrasives, is called "scouring." People used to use scouring-rush, sand, or baking soda for this.  I've seen salt or sugar-based scouring stuff lately, especially for the shower; you can do the same for glass carbuoys, when you have some gunge in there that isn't easy to get out with a brush, put some rock salt in there with a tiny bit of hot water, and swish it around like a rock-polisher.  Takes a while, but gets it done.  
I don't like it as much, because it can scratch the surfaces you are trying to clean, which leads to it being easier to stain or dirty in future.  Also note that baking soda, while OK for people in modest quantities, contains a lot of sodium which is a plant toxin.
 
If you're doing non-toxic cleaners for the good of the planet, not just your own chemical exposure, it's good to know what minerals are safer for plants in your area.  In some inland areas, a little phosphorus is much appreciated by plants, where boron is excess and suppresses growth.  Right on the coast, most plants are adapted to excess sodium; but not so inland.  Ag schools' extension services can give you the lowdown for your area, or you can do soil samples if you're really into details.

I do use biodegradable dish soaps or detergents for routine dishwashing, combined with very hot water, so I don't need much.  Apparently it's working for the plant life outside our greywater dish station, at any rate.

Final tip from a brief season in an organic winery: Wash promptly.  
If everything is rinsed immediately, with hot water, and dried as soon as possible, you don't need to use chemical sterilants to kill unwanted films and colonies of unwanted life... because you don't provide it food or habitat.

Now ask me, does my kitchen reflect all this lovely-sounding advice?
[two guesses...]

-Erica

I have a specific small cotton cloth that I use when canning to wipe the edge of the jar before sealing. I boil that cloth in with the empty jars for 10 min, use it to clean the rims, rinse it with fresh water, then toss it back in with the filled jars for however long I'm doing the boiling water bath. I then hang it to dry thoroughly before putting it away until the next canning session. The instructions all say to use paper towel for cleaning the rim, but who's to say that the paper towel is sterile?
Hot water works for me!

I find the instant-scalding technique and regular change of cloth/paper to be a good technique for keeping beer-brewing equipment clean without using any chemical agents.
Same for kombucha and kefir equipment.

The carbon-footprint of various detergents and cleaning products is very high, adding to the energy used by hot water and the polluted water.

Instant application of scalding water costs no extra energy if your household sees a constant stream of teas, coffees and hot water bottles.

Washing your hands can often be avoided if you keep newspaper handy around the house and garden as a makeshift-glove.

steel wool, baking soda and boiling water is my preferred cleaning method but i still would like to acquire a good steam cleaning system. not one of those plastic handheld units - the small industrial types like dupray.

Water is actually a very poor wetting agent and usually needs a soap or detergrent to lower its surface tension to make it an effective cleaner

In almost all situations where I'm going to use a soap or detergent, I first wash the item with pure water. I almost never heat that water.

If I'm doing dishes, they are often already soaking in cold water. That water is drained and then everything is given a run under the cold water tap. This way, I'm not pollutant my hot or warm soapy water with stuff that could be easily rinsed off. Very little soap is required when dishes are already pretty clean.

I have a simple top-loading RV style washing machine that doesn't lock me out in the middle of the cycle. Before any soap is used, really dirty stuff is given a few minutes in pure water and then the machine is drained. There's no shortage of water and the thing uses almost no electricity. So I'm saving soap. The machine uses one kilowatt hour of electricity every 4 hours of use. With an average wash time of 15 minutes, that's 16 loads on about $0.12 worth of electricity.

After clothing is pre-washed, I usually use about $0.03 worth of homemade soap for the wash cycle, and then it is rinsed in pure water again.

Work clothing is often washed in pure water, without any soap. They may not be perfectly clean,  but certainly cleaner than if nothing was done. I'm just trying to get rid of the mud and most of the stink. On hot days I may put the same clothing in for a quick rinse and spin, three times a day, then I put them on damp, as a wearable swamp cooler.