Greywater is the term that refers to the water that is used but not unduly contaminate -- water from washing dishes or clothes. I have been collecting my dishwater in a large bucket, about 5 gallons. I collect the rinse water in a tub in the sink and empty it into the larger tub as necessary. I put the hot water in a smaller tub.
One caution-- the microorganisms in soil do not like detergents because they damage cell walls and can kill the microorganisms. They also dislike strong detergents for the same reason. Microorganisms in soil areal to healthy soil that holds nutrientuntil they are needed. Therefore, I am as kind to them as I can be. I use Meyers or a similar environmentally friendly detergent such as Dr. Bonner's. I don't put it into the water directly because that requires a lot more detergent for the same detergent action. Instead, I use an abrasive pad and apply a coupkle drops at a time. If the dishes need soaking, I soak them in the rinse water or in the fot water that I use for washing.
A related matter, how important is hot rinse water? Many years ago, the folklore was tthat hot rinse water kills germs. While it may stun them, if the water is hot enough for you to tolerate on your hands, it is not killing many germs, so you might as well use cold water. The detergent makes it impossible for germs to stick to the dishes. That is why it is nice ti have your soap concentrated at the surface of the dish instead of in the wash water.
Do automatic dishwashers save energy and water? They don't if you do dishes my way, but if you mindlessly run hot water, you are much better off with an automatic dishwasher. However, I don't care for the lingering taste of the detergents used with automatic dishwashers and my plants seem to be doing better with dishwater than they did with tap water and an occasional shot of fish emulsion or other natural sources of nutrients.
I make the water even more nutrient rich by using very hot water to sterilize cotton disrags before I begin washing. Rather than set my hot water heater at a higher setting than I need for most uses, I heat my dishwater in a tea kettle over my pilot light, insulated by an upside down pot. The water is far too hot for my hands, so the first stage is taken care of with spoons. My dishrags are also grey but they never smell bad.
Inaugment the dishwater with water from the laundry. I have a top loader, also said to be wasteful of energy and water. While this may be true for others, it is not true in my world. Again I use a mild detergent. I have a suds saver setting, so I use the same detergent at least twice. Though one could also use twin laundry tubs, I use a walk-in tub with lots of capacity, catching the detergent in a large plastic tub that sits on the seating area. I collect all the wash water, and when I combine this with my collected rainwater and my dishwater, I almost never need to resort to turning on the tap and my plants are thriving.