How are red dwarf stars formed?
Pretty much like any other star... read on!
The size and colour of stars is essentially a matter of the quantity of matter in the star. Essentially what happens is the pull of gravity draws the gas into a highly compressed ball. As this crushing pressure increases, so does the temperature of the gas. At a certain critical temperature, fusion is able to begin, and the star starts to emit light. But as the temperature increases, the hotter gas then builds pressure, causing it to expand outward, until an equilibrium is reached, and the star achieves a stable radius, whether dwarf or giant.
The colour is related to the temperature of the gas ball. Red is the coolest star, while blue-white is the hottest.
Because they are cool, they consume their fusionable material very slowly, and so are very long-lived stars, resulting in one of the most common features of the cosmos.