Just stretch a line between two sturdy objects and clothespin a tarp to it.  Having a 2-gallon bucket or something for it to drain into would be handy.
Even in the desert, after it's rained for a few minutes, there's much less dust/sand in the air.  You could just strain it through a bandana or coffee filter.
Rainwater is far cleaner than ANY groundwater.  I wouldn't worry about contaminants.  What you're probably getting from your municipal supply or well is probably far filthier, you just don't know it.  Ignorance is bliss, right?
Sue