Where does the dust on the Moon come from? From the Apollo missions we know that the Moon is covered with dust. Where does it come from? Is it from the erosion of Moon rocks? By what? Or by accretion of dust from space? Which comes from where?
 A: From wikipedia : 
The physical properties of lunar soil are primarily the result of mechanical disintegration of basaltic and anorthositic rock, caused by continuous meteoric impact and bombardment by interstellar charged atomic particles over billions of years. The process is largely one of mechanical erosion in which the particles are ground to finer and finer size over time. 
A: As Ravachol quoted, the material on the surface of the moon is mainly the result of billions of years of micrometeorite impacts onto larger rocks on the lunar surface.  We call this material "regolith" as opposed to "soil" because the latter term is used in geology to indicate a more biological/organic origin.  "Regolith" should technically be used to describe the surface material on all surfaces except Earth, but even planetary scientists will slip from time-to-time.
The process of creating regolith is usually referred to as "gardening" because the surface material is hit by extraplanetary/lunar material, it will be broken up and tend to move a little, and then the material underneath it can be hit.  This in general creates a process of slow overturn where the upper several meters will be broken up regolith before you hit more competent rock.  However, the depth of the regolith can change significantly over the surface of the moon.
It's also not just created by the micrometeorite impacts, but also larger impacts.  A 1-km-diameter crater will produce a layer of ejecta that, after about 1 billion years, will become generally indistinguishable from the surrounding regolith except for maybe a slight topographic difference (ramp as you approach the crater rim).  These larger impacts are rarer, but they do create significantly more future regolith material than the micrometeorite bombardment in one go.
And yes, to a lesser extent, cosmic rays and solar wind will help generate regolith, but they are very minor compared with actual meteoritic material.  Also, you can have tidal forces and some seismic activity (mostly from tidal forces) that will add to this, but those are also very minor.
