Well...interstellar dust comes from a variety of sources, but mostly from the atmospheres of very old stars. In the outer layers of these red giant and red supergiant stars, the temperatures are so low that dust grains made of silicon monoxide or graphite can condense like rain drops directly from the stars material. The dust grains are whafted into space by radiation pressure or by some mechanical means, and over billions of years and millions of stars, they form a persistent 'medium' of dust grains everywhere. As they collect along with interstellar hydrogen gas, into vast clouds, their surfaces become very chemically active and they serve as catalysts for forming complex molecules in the interstellar medium. Dust grains are the repository of most of the interstellar medium's 'heavy elements' beyond helium. There seems to be very little dust in intergalactic space, and most of the dust we can detect seems to reside within galaxies to one degree or another. Elliptical galaxies seem nt to have much of an interstellar medium at all, while some spiral galaxies are so loaded with dust that it extinguishes a significant fraction of the light from the other stars in the galaxy. Some galaxies have such tremendous episodes of star formation occurring that the dust in these galaxies converts nearly 100 percent of the light into infrared radiation and so you get ultra luminous galaxies in the infrared, but which are very hard to detect at optical wavelengths. Typical interstellar dust grains are about 1/2 of a micron in diameter, but can grow up to several microns or more in the deep dark cores of collapsing dust clouds. Eventually these dust grains stick together to form ever larger bodies all the way up to asteroids and planets!