Welcome, Bob, to gardening in Arizona. It's totally different than PA or FL. Your grass is likely bermuda grass. So spading and roto-tilling it to get rid of it won't work. believe me, it'll come back. That bermuda will grow through concrete. However, being from FL, you may already know this.

I'd suggest Round-Up to get rid of bermuda, but I'm not much of a super organic gardener. Lots of folks on this forum are, though. I'm sure that they'll chime in with some suggestions. Assuming that you DO have bermuda grass, it's dormant this time of year. So you have to wait for it to break dormancy to kill it.

The only way I know of to cut down on the dust factor is to put some sort of mulch over the plain old dirt. Lots of people use rock mulch (me included). You could also use organic mulch or compost. On windy days, it may blow around a bit. I use organic mulch to cover the ground on the veggie part of my backyard garden. In other areas, I just use rock mulch.

Thanks for the reply. I am hoping it wasn't Bermuda-I tried to identify it-it just didn't seem to fit on the ID site=more like a weed or zoysia (sp)but simalar to bermuda. It sure was ugly grass. I thought round-up would work but I just hated to spray in an area to grow veggies.
No room for a compost pile-Home Depot for me. It just gets so dry so fast here-I am worried even the compost will blow around.

Thanks again

If your soil is hard, it could have a high clay content. If it isn't in an area where you walk much, you could soak it down an inch or two and cross your fingers that the top part solidifies back into clay when it dries. Not a perfect solution, but a little less dusty, anyway. Then as you add amendments that should help take care of some of the dustiness too.

You could lay down straw or large size bark. Even small size bark or shredded mulch might work if you put enough down. In any case, you should be able to rake it back in spring to lay out your rows - or whatever. You could till some of it in and probably improve the soil.

http://www.ourgardengang.com/lasagna_gardening.htm

Here's a link for lasagna gardening. You just lay down newspaper over the grass and cover with dirt several layers thick...kills the grass and encourages worms to keep your soil moist and areiated. Try it!

Thanks for all the suggestions. I was going to try cypress mulch or pine bark mulch for walking in the rows-does that stuff break down here? The cypress bark mulch lasted a shorter time in Florida than the pine bark. I don't even know if they are available here as yet.

I could be doing the Lasasna Gardening if that grass doesn't die....

I am not a strict organic gardner-I just like to avoid the herbicides and insecticides. I will probably use fertilizers. I like Miracle Grow.

Thanks