In order to make your own fabric paint, you need some very basic ingredients, some water, pigments, milk or milk powder, and a sense of adventure. There is no 'right' or 'wrong' about this - it either works or it doesn't. Fabric painting and fabric paints are a go/no-go system.
First you need to decide if you are going to need to wash the fabric after painting it, and if so, how often will you need to wash it? If you're making a wall-hanging, you aren't going to wash it as often as if you are making a shirt, obviously.
In US Colonial times, paints were homemade, and you can find formulas for making several different kinds of good paints on various web sites or in books on colonial life skills at any good library. If your library doesn't have anything, ask the reference librarian to do a search for suitable titles and get books for you on Interlibrary Loan.
My favorite paint is milk paint, because the casein in milk is waterproof when dry, and it is pretty flexible. You can buy milk paint pigments from artist supply houses, many of which has online catalogues with color swatches to look at. The color range is pretty wide, and you can mix pigments to make shades to suit yourself.
Basically, you mix the pigment with water to the desired consistency, and paint away. You determine the desired consistency by experimenting with small swatches of your fabric; the same as they did in Colonial times.
You can also make your own milk paint pigments from powdered clays and mineral ores. This is more work, but it can be very worthwhile, especially if you are an artist or a restorer, as I am. You can either get milk from a dairy farm if you live in a dairy farming area, or you can use powdered milk, keeping mind that low-fat powder will give different results from whole-milk powder. The fat makes a difference in both the color retention of the paint and in how the paint sticks to the fabric. Again, you will have to experiment to see what works and how various combinations work.
To mix the paint, you need to sieve the powder to eliminate any lumps of pigment, since they won't mix with the water properly. You should mix the pigment and water in a container that is large enough to contain spatters, because you need to mix the paint vigorously. My favorite method of mixing is an old drill and a paint-mixer that fits in the chuck.
If you are only making a small amount of paint, you could use a wire whisk or a hand-held mixer and beaters. Just remember to use a large-enough container to keep the spatters in. There's no sense wasting this paint..
Once the paint is mixed, you need to strain it through about 4 layers of cheesecloth to get rid of any lumps that formed while you made the paint, and then you can begin applying it.
When you wash your fabric before you paint, be sure NOT to use fabric softener of any kind. Fabric softener, whether sheet or liquid, will interfere with the paint and keep it from bonding with the fabric so the piece is water-resistant or waterproof when dry. Depending on the fabric, milk paints, being water-based, will either soak in and spread out - spread more if they are too thin - or they will not soak in but will just sit on the fabric. If your paint is too thin, either add more pigment or let it sit awhile in shade with the cover off so some of the water can evaporate.
Experiment with different methods of applying the paint - brushes, sponges, rags, twigs, bones, for example.
Here's a tip you can use with dark colors which will make your milk paint more water-resistant.. talk to a butcher or a slaughter house and get some blood to put in it. Dried blood is the very dickens to get out of fabric.
If you don't like the above method of making homemade fabric paint, you can always collect liquids that stain, such as wine or fruit juice. Kool-Aid powder can be pretty tough to get out of fabrics, so it can be used to make a fabric painting, too.
This is about creativity, not meeting some preset 'standard' for what is right or wrong like when you were in kindergarten, so experiment. You will never know what you can do if you don't putter with it. Experiments make fine fire-starters and pet bedding, by the way. If the piece you don't like is big enough, you can cover your plants when frost threatens. Nothing that doesn't turn out so you like it isn't necessarily garbage. And most of all, have fun!