I started by replacing the most used products with products that were safer. The first item that I changed was the dish soap since my hands were in it all day long. After a long experimentation period, my beloved Dawn was replaced with Seventh Generation dish soap.
I was blown away by the price differences of everything. It seemed that many of the green cleaners were at least 2-4 times the cost of the chemical cleaners. So I attended a friend's DIY Green Cleaning workshop and started making my own recipes that surprisingly worked great. I used the recipes from Care2.org to make my own green cleaning kit with supplies that I mostly already had. I have also learned some great cleaning tips over time such as a damp microfiber cloth is great for dusting and that my wood furniture only needs to be oiled (with a natural oil) once a year! My hard floors are cleaned with a steam mop that cleans with only water and the cloths go in the washing machine to be reused for years so there is no waste. Dryer balls make my clothes soft without coating them with chemicals and last for several years. Vinegar, baking soda, and Dr. Bronner's castille soap are the main cleaning items in my cleaning bin and I love it! Keeping my bathroom ventilated while showering with "air-in" and "air-out" prevents mold (for example an open window and the fan -- or -- an open door and the fan).
For the cleaning products that I do buy, I like to support companies that are green because they know that it is best for the environment and the next generation. That is why I don't buy brands such as Clorox Green Works and I suggest that you don't either. Stick to the wholesome companies like Seventh Generation, Earth Friendly Products, BioKleen, Ecover, etc.
The best part of green cleaning is that our kids mimic us. When they see us do something they want to do it to. I have no issues handing one of my older kids a rag to help me clean because I know that I am not exposing them to any extra chemicals that can disrupt their immune system or behavior.