To go No Poo is to stop using shampoo. Why would you want to do this?

1. Shampoo is expensive.
2. Chemicals* in shampoo can irritate and dry out your scalp and hair.
3. Chemicals* in shampoo can be hazardous to your health.
4. Your body produces oil to naturally condition your hair and keep it healthy. Using shampoo daily upsets the natural balance and causes you to produce more oil than necessary to compensate.

When you stop using shampoo, you will probably experience a transitional period while your body gradually adjusts to produce just enough oil to keep your hair healthy. During this time, which can range from a few days to a few months, you'll probably have some extra oil and grease that you may want to take care of to look presentable. The cheapest and most effective way to handle this is to use baking soda. The method I use involves a plastic cup, some baking soda, and a shower. You may also want to condition your hair after using the baking soda mixture, as sometimes it can leave your hair a bit dry. There are lots of different ways to do this; I use apple cider vinegar.

* In this context I'm referring to certain synthetic chemicals which have proven harmful in specific circumstances. I'll let you look up each one in the ingredients on your shampoo on your own. Your shampoo might not have anything you don't like in it after all, although the other benefits of going no poo still apply. Please keep in mind that literally every substance can be referred to as a chemical and many are not generally harmful (water, for instance).

Step 1: Cleaning

Put 1-2 tbsp of baking soda into a 16oz cup (or close). The ideal ratio is about 1 tbsp of baking soda per 1 cup of water. When you get in the shower, fill the rest of the cup with water and stir until the baking soda is dissolved. You should have some cloudy water at this point. If the mixture feels gritty or pasty, either add more water or use less baking soda. Now apply the mixture to your hair. Ideally, you should aim to get most of it around your roots and work it in with your fingers, gradually distributing it throughout the rest of your hair. It won't lather like shampoo, but it does give your hair a distinct "smooth" feeling when it's properly distributed. Once you've rubbed it around a bit, you should be ready to rinse. When you are completely rinsed you are ready to condition.

Step 2: Conditioning

The simplest way to condition is to use apple cider vinegar, in about the same way as you used baking soda: 1 tbsp of the vinegar per 1 cup of water. If you like you can add a few drops of your favorite essential oil, some honey, or some lemon juice. When you've mixed up your conditioner, pour it on and work it in just like you did the baking soda. When you're satisfied, rinse thoroughly.

Step 3: Closing Thoughts and Advice

I hate the smell of vinegar. However, apple cider vinegar isn't as harsh as white vinegar, and after you rinse and dry your hair, the smell is completely gone. Your hair will smell like hair, or maybe whatever you added to your conditioner.
The eventual aim of this process is to let your natural oils care for your hair, so you should use the baking soda and vinegar only as much as you need it, hopefully reducing your usage to zero eventually. Good luck, and don't give up!