I think raised beds would be a good way to go.
Having lived in Arizona I know the soil isn't prime planting soil. Buying enough dirt to fill the raised beds could get expensive so you can always try to find free dirt/compost and mulch.
Another idea that would take a little while would be to begin changing your ground into good soil by adding manure/compost, working it in and after a year you should be able to plant in the soil. Just remember that some things you would plant (even tomatoes) will need to be planted deep. When you put maters in the ground it is recommended to bury about 75% of your plant.
Do you have any compost piles going? We have 2 compost bins and 3 piles here. Great way to get premium soil and great way to rid yourself of kitchen scraps (no bones, no dairy and no animal fats) but any veggies/fruits, egg shells, dryer lint, even human hair can be composted.
Make sure your garden will have plenty of shade. Lots of plants won't produce fruit if the temperature is too high and you don't want to lose any plants or fruits to sun scald.
ALX has lots of gardening experience, I'm sure he'll be along eventually to offer some advice.