If you want to make your own soap, find a recipe and directions online for soapmaking. Basically, you take some lye (dangerous, use caution), mix it with solid or liquid fats. The proportions and exact directions would be on the recipe you find online. I did this for an 11th-grade science project. You get ivory soap, so to speak.
Unless you really want to do the chemistry project, why not use a soap with no additives? Dr. Bronners (saponified fats) and Charlie's Soap (surfactant only) are examples that you can look up and see if you like their ingredients.
You can't use a sudsing soap in a washing machine or dishwasher. If you do, you'll get suds all over the house.
Don't expect your laundry to end up all fluffy. In a hard water area, your towels will end up kinda cardboard-y. Your family won't like it, I reckon.
The no-soap alternatives are (1) take clothes to the river and beat them on the rocks, (2) vinegar is a good cleaner, but I've never used it on the laundry.
I always have tons of leftover animal fat. I was thinking about making my own soap, but it seems like a hassle. I use the fat for awesome tallow lamps. Adding a wick is much easier than making soap.
P.S. If you are getting soap film in your dishwasher, you are not using the correct dish washing detergent for the water hardness in your area.
