The best model for the origin of earth's moon is the following:

About 4520 million years ago, an object perhaps the size of mars or about 10-15 % the mass of current day Earth collide with the protoearth. This collision was not a direct head on but instead a glancing blow. This gigantic collision put about 1/80 of the total mass of projectile plus embryo protoearth into a circular equatorial orbit around the earth. Stuff in this debris ring within about 100,000 to a million years coagulated to form the moon. Since that time, tidal forces between the moon and earth have acted to increase the earth- moon distance to its present radius of about 380,000 km. The moon is receding from earth at rate of about 2 cm/year. This is being measured continuously since 1969 using a laser beam and a mirror left on lunar surface by astronauts.

I'm not sure we know. There was a theory running around for a long time that a Mars-sized planetoid hit the Earth about 4.4 billion years ago and that the moon is just splash from that impact that collected in orbit. This was supported by the lower density of the moon (the moon does not have a large iron core, unlike the Earth, which would happen if it splashed off of the Earth's surface), and by various computer models. However, I believe this theory has come under some debate, and I don't know what (if any) conclusion that debate came to.