Objects in space, including stars and planets, are formed by a process called accretion. Accretion occurs when small particles in space attract each other due to gravity, and begin colliding and clumping into larger particles. After a long, long time, enough particles merge together to become the size of a planet or star.

Moons can either form from accretion and then become trapped in the orbit of larger planets, or they can form when a body collides with a planet with enough force to eject material into the orbit of the planet. It has been proposed that the earth’s moon formed after a body approximately the size of mars collided with the earth (although scientists still don’t all agree on how our moon was formed).

Good question. Nebulae are diffuse clouds of gas and dust in space that are drawn together by gravity. If a clump of matter gets dense enough, then the gravity can pull it together where it becomes a star. Other clumps of gas and dust tend to coalesce around forming stars, too, which makes the planets, moons, etc. That tend to orbit stars. Exactly how this happens is still up to some debate, however.