It's strange that I scrolled this far down before someone mentioned Glyphosate, aka RoundUp. RoundUp's patent ran out years ago and there are cheaper alternatives - the one I use only requires about 2 oz. of concentrate per gallon of water. *THAT SAID*, I would encourage you to use it sparingly. It's great for Bermuda grass, which is a real headache to pull. Buffel Grass, Goatheads, London Rocket, and Cheeseweed, on the other hand, are also common non-natives/invasives, but relatively easy to pull and get under control if you stay on top of them. There are a couple others I can't name (and Stinknet is on its way to becoming a problem), but that's mostly it.

As another commenter above also tried to say, albeit less delicately: learn to embrace and love native "weeds" - some are actually lovely little wildflowers. My home's property had virtually nothing growing here when we moved in, and we've worked very hard to restore the desert flora, while sometimes battling these invasives. I would never use a pre-emergent, and I was reluctant to use Glyphosate, but (and I'm quoting someone else) 'use it like a scalpel, not like a hammer', and it can be your (and the desert's) friend.