First, I'd like to thank my mom for teaching me to do this. I've met a few people who grew up with dish washers, and weren't really sure how to do this when they got their first cheap apartment without one. I thought I'd write this for other people in the same boat. If nothing else, it may save a few roommate relationships.
Now take a look at the picture. This is my setup. I have the drain rack on the counter, and keep the dirty dishes on one side of the divided sink. If you need to conserve water the drain rack should really be in the sink, to allow you to rise the whole rack of dishes at once. The drain rack I have doesn't fit in this sink, so I'm doing it this way.
1. Dish Soap - Just about any brand works. You'll need to use a little more of some of the cheaper ones.
2. Drain rack - You can buy these in big box stores and hardware stores
3. Plastic net puff scrubber - These work pretty well, and dry quickly, but gunk tends to get stuck in them, especially cooked egg.
4. Dish Brush - These are good for knocking the big chunks off. They are great for pre-washing for the dish washer, or knocking things into the garbage disposal, but they don't really get the crusty bits off very well. If you want one, look for one that has a straight edge you can use to scrape with.
5. Dish cloth - This is the traditional tool. They are good for wiping down counters, and you can use them to wash dishes. They have some limitations. Because they are absorbent, germs grow on them if you aren't careful. You need to wash them out with soap after each use, and boil them, or put them in the microwave soaking wet to kill germs. DON'T MICROWAVE A DRY DISH TOWEL or SPONGE. You will start a fire. You should also hang them to dry between uses.
6. Sponge - I don't have one at the moment. These are a lot like dish cloths in use and maintenance, but they don't dry as fast.
7. Green scrubber pad - These are my favorite for dish washing. They scrub well, dry quickly, and don't get too much food stuck in them.
Step 1: Fill the Dishpan/sink
In these instructions, I'm using a double sink. If you don't have a double sink, that's not a problem. Instead of filling one side of the sink, use a plastic dish pan. If you don't have a plastic dish pan, use the biggest widest pot or bowl you have.
1. Wipe out the sink and rinse
2. Plug the drain. If you don't have a plug, go to the hardware store. This one came with the apartment. If you're buying, I'd go for the cheap flat rubber one that fits all sized drains.
3. Add some dish soap right under where the water is going to hit. About two teaspoons works with this soap and this size sink. The amount needed varies with the brand and the dish pan size. You're aiming for just enough soap to cause suds to cover the top of the water.
4. Fill the sink about 1/3 with bath temperature water. You want hot water, because hot water cuts oils.