Stars form when clouds of interstellar dust and gas collapse in on themselves and heat up, eventually leading to the nuclear fusion of hydrogen into helium. Several stars typically form out of a single cloud, making star clusters extremely common.
According to NASA, stars are formed when clouds of gas and other material either gain sufficient mass to begin a gravitation collapse or are acted on by an outside source. The shock-wave from a nearby supernova or the close approach of a neighboring galaxy are two suspected triggers for inducing a gravitational collapse. The collapse begins concentrating portions of the cloud into dense knots of material. As more material is drawn in and compressed, the center of the knot begins to heat up, and once the outward pressure of the compressed material equals the gravitation pull of material coming in, a proto-star is born.
All of the material present at the time of star formation does not go into the creation of the star. Much of the original knot of material still surrounds the proto-star. Radiating outward in a flattened disk, and this material may eventually coalesce into planets, moons, asteroids or comets. New technology has allowed astronomers to catch glimpses of this process in action, and x-ray telescopes have taken images of the knots of gas themselves forming, ordinarily invisible inside the cloud of gas and dust.