So, having found out where they were, we shall consider what they are. The best clue to finding out what they're made of is to examine those asteroids that come down through Earth's atmosphere, at which point they are known as metorites. As described in the next section, many meteorite fragments have been found on Earth (just look for the craters!), so it's been a simple matter of physical and chemical analysis to discover what they're made of.
There are basically two types of meteorites:
aerolites - which are largely made up of rock and other silicates;
siderites - which are made up of a metallic nickel-iron alloy.
It's probably safe to assume that asteroids as a whole share these types of composition as well. How they came to be made up that way is still debated - some think that the Asteroid Belt was left-over matter from the formation of the planets, some think it might be the remains of a planet that met a particularly destructive end, maybe at the hands of a comet or another asteroid from outside the Solar System.