Making paints and pastels at home has become popular among artists for several reasons, including cost savings and a greater degree of control over the final product. While pigments can be expensive, they are easy to store and can be used in small amounts as they are needed, and linseed oil is relatively inexpensive. Artists who mix their paints at home have more control over the composition of the paint than artists who purchase prepackaged paints.
To make oil paints, pigments are mixed with linseed oil to produce a paint with the right consistency. Oil paints can be easily made at home by purchasing both pigments and oil and mixing them together. It is important to add the oil to the pigment -- and not the other way around -- since only a small amount of oil is needed to make a usable amount of paint. Attempting to add pigment to oil will likely result in making too much paint.
The process of making paints with other binding agents is much like the process for making oil paints. For tempera paints, for example, the pigments are mixed with egg yolks. Watercolors are made slightly differently, by grinding pigments with a material like gum arabic and a wet material that will evaporate such as grain alcohol to produce a water-soluble paint that can be stored dry for a long period of time.
Pastels are more difficult to make, since they need to be more of a stick than a liquid. To make pastels, you need to grind the pigments with a material like gum tragacanth (for pigments that don't bind together well), a stabilizing agent such as talc or calcium carbonate and distilled water. The goal in making pastels is to create material with a dough-like consistency that can be rolled into sticks of individual color and dried.