Wash While Cooking -- While cooking wash as many dishes as you go, of course there are last minute things that won't be possible to wash but at least give them a scrap and get some water into them to soak while you have dinner.
Scrape and Stack -- To ready things for washing and to avoid dirtying your the water for washing right away, begin by scraping the dishes of excess food. Stack the dishes in preparation for washing. Food that is stuck on may need to be soaked first before washing. I use one of these little handy plastic scrapers. (I got it our local kitchen specialty shop in the mall for 95 cents. But here is one that is similar. They are also great at getting gummy labels off such as price tags on the glass of picture frames.)
Stack similar dishes with each other and in the order they will be washed. Such as glasses, cups, silverware and then plates, bowls, serving dishes and finally pots and pans. You are placing them from lightly soiled to heavily soiled and those soaking.
Prepare the area and water for washing dishes -- After dinner, make sure you start by cleaning area - the sink where they will be washed, the sink that they are rinsed (if you have a double sink), the dishrack and mat under it all should be clean. If you don't have a dishrack just place a thick dish towel down to catch drips.
Gather clean a dishcloth, sponge, bottle brushes or anything else that you use when washing the dishes. Then fill the sink 2/3 with with water. Make sure it is hot. I think I read in Home Comforts that the water should be hot enough that your hands are slightly uncomfortable if you were to leave your hands in the water. Wearing gloves will help you deal with the heat of the water as well protect your skin. Add your suds at anytime when filling your sink.
Washing Dishes -- As I stated in scrapping and stacking, start washing the lightly soiled items first. Usually this includes flatware, glasses and cups. By doing in order from lightly soiled to heavily soiled it helps keep your water fresh longer. Put a few dishes into the water at time so that they have some time soaking while washing another dish. Now move on to the washing the plates, bowls and serving dishes. Keep an eye out for when you should change the dish washing water. Usually I change mine right before starting the next group of dirty dishes which is pots and pans. If I had them soaking, draining the sink to prepare it with new water also allows me to scrap any more bits of food down the garbage disposal before starting to refill with clean water.
Scrub all dishes with slight pressure under the water. Food lifts off easier if you wash them under the water. Life them out to check if they are clean every so often. To find out of your dishes are clean you will need to touch them as well as look at them. When you touch them you are more likely to catch residue or oiliness. Also as soon as your water feels oily, looks unclean or doesn't have suds - drain and refill.
Rinse dishes -- If you have a double sink, use it to rinse the dishes. If you don't a double sink, then you can use a dish pan filled with hot water to rinse/dip your dishes clean. Hot water rinse not only gets suds off but kills microorganisms/bacteria and speeds drying. Rinse dishes before they have a chance to dry after washing.
Hand Dry Dishes or Air Dry Dishes - When hand drying dishes use a fresh clean towel and change the towel when it becomes damp or soiled. You might go through several towels in hand drying dishes. You should never use the towel for your hands or to wipe counters off and then go back to drying dishes. Use the fresh clean towel only for drying the dishes. Towel dry until the dish feels dry and shows no spots or lint.
Draining is important for air drying dishes. You don't want water trapped under a cup or bowl as it can cause bacteria to grow. So makes sure that all your dishes are tilted slightly so that water is not trapped under them or doesn't pool in them also.
Put away dishes and clean supplies and area -- Put dishes away as soon as possible as leaving them out puts them at risk of dust, germs and breakage. Wipe down the sink and dish rack/drainer. Wash and dry the dishpan. Make sure to remove rags, dish cloths, or sponges from the kitchen area as someone might be tempted to use them and they need to be replaced. I leave them in a laundry room to air dry or throw them directly into the washer.
Now you can go and relax!