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