Both watercolor and gouache use gum arabic as the main binder ingredient in the paint. Watercolor can be the most difficult to get right since you want it to thin down nicely and work well in washes. With gouache that's less a problem so it's probably the easiest of all paints to make. The only issue is finding all the ingredients. Essentially you just mix it all together and start painting. If you paint in gouache exclusively or often, you'll find making your own paint a more economical option than buying commercial brands off the shelf. The recipe below gives me good results with any pigment.
BINDER:
2 tablespoons gum arabic powder
4 tablespoons distilled water
Pour water in a blender and add powder slowly while blending. Let sit 1 hour and spoon off any foam. A faster method is to heat the water to boiling, add gum slowly while stirring, let cool to room temperature. The blender often gives me a clearer liquid. Strain liquid through a cheesecloth if it's lumpy.
3 ounces honey and water (1:1) warmed into solution
3 ounces glycerin
1 teaspoon oxgall (optional)
3 teaspoons dextrin powder
Mix together in a warmed bowl and add in gum arabic solution slowly while stirring.
1-2 drops preservative: Oil of clove, Thymol, or even concentrated Lysol will work
PAINT:
2-4 tablespoons dry pigment
1-2 tablespoons Binder
1 teaspoon Calcium carbonate as an optional filler to help bulk up thin paint
Place pigment on a large clean glass or plexiglass plate. I usually dump out about 1 teaspoon of pigment at a time, which is shown below.
Make an indentation in the pigment pile. Add a small amount of binder solution and mix together thoroughly. A good target is half as much binder as pigment (1:2) but some pigments require less. Keep adding just enough binder to make a smooth paint to your liking.
Spread out a swatch of fresh paint on a clean spot of the mixing plate. I typically just rub some of it with my finger making about a 1 inch circle. Let that air dry for several minutes COMPLETELY (this will likely take longer than you think - give it 20-30 minutes or so.) Rub the dried paint with a cloth. If paint completely lifts then the mixture is too weak or there's not enough binder. A little staining on the cloth is acceptable. If the dried paint has cracks then it has too much binder. Those can be hairline cracks, so I like to make a high-res computer scan of the dried paint to be certain.
Notes:
If the pigment paste is too rough or grainy you may need to grind it down some. Large glass mullers are okay if you plan on making lots of paint, but a small porcelain mortar and pestle will do a good job for small amounts. Grinding is often not necessary. A small flexible spatula or palette knife often works well enough.
Hunt online for good prices on gum arabic, sometimes @ $12-15 a pound. You can find it already in liquid form but at higher cost.
The honey water mixture can be optional, but is extremely easy to find, plus it seems to aid with blending characteristics of the paint.
Dextrin is used in brewing beer, dying fabrics, and pyrotechnics, so shop around. It typically comes from corn and can be the hardest thing to find sometimes. Other starches might substitute, like rice. Store these powders in a dry area kept at a comfortable room temperature.
Oxgall (from the gall bladder of oxen) improves paint absorbancy and the wetting of pigments. It is often sold diluted in jars at art stores in their watercolor section. Grain alcohol or denatured alcohol can also help with wetting the pigments. You could leave these out of the binder mixture and only add them when necessary while making paint. Even for pigments that don't need it, it won't hurt anything by being there.
Using a preservative will extend the paint to several years storage and help protect against pests and mold. Thymol (oil of thyme) is sold for finger or toenail fungal treatment and as an insecticide, so check in drugstores or garden supply. They can slow down the drying time somewhat, especially oil of cloves.
There are commercial brands of ready made binders (if you're lazy

) from Schmincke, Sennelier and Maimeri (possibly others.) I've never used any of these personally, but they're available if you want to try them.
There are also commercial watercolor binders; although, they likely will not contain dextrin which aids adhesion of the higher pigment load, and keeps the mixed paint from getting too stringy.
I've used this mixture over the years many times. I welcome others to test it out and let me know how it works for them.