Everything (Sun, planets, asteroids, comets) was created 4.5 billion years ago. The material making up the Solar System all came from a single homogeneous cloud of material. This cloud of material became gravitationally unstable, and underwent gravitational collapse (1). The cloud of material will begin to spin as it collapses, becoming splayed out in a disk due to the angular momentum (2). Innumerable small particles of dust will begin to condense out of the surrounding gas, one atom at a time. The solar nebular dust grains, while still small, will grow rapidly by this process.

Accretion begins
Adding one atom at a time (condensation) is fine when the grain is small, but once the grains get to be fairly large, such a method is inefficient. The density of grains is still quite high while they are relatively small. The grains will attract to each other, mostly through electrostatic charges built up on their surfaces. This pulls them together, causing them to collide. Depending on the surface composition, most will stick together, thereby increasing the overall grain size. This process is called accretion.

The Formation of Planetesimals
Accretion continues and the particles in the solar nebula gain mass. At some point, these constantly growing grains grow large enough to be deemed planetesimals. Planetesimals can grow to fairly large size, several km. Now their gravitational attraction is significant enough to attract grains and smaller planetesimals nearby. In this way, larger planetesimals just keep getting larger, sweeping up and capturing all the smaller particles in its local area.