Can I put grass seed down to get a nice lawn or do I have to till the

You should be able to "overseed" the existing lawn, sprinkle the grass seed like you are feeding chickens and water it

You can use a machine that removes plugs which makes little holes for the seed and fertilizer to enter the lawn. The best time to do this is in the fall season. Check it out on This Old House website.

Having a lush lawn in Arizona is a challenge, but can be done. Here are some Arizona specific sites.

http://apnursery.com/blog/lawn-care-tips-for-arizona/

http://www.goodmanslandscape.com/blog/tag/phoenix-summer-lawn/

https://www.pinterest.com/pin/444800900673401474/

I live in a similar climate and am planting clover in my back yard, easy care for the long blazing hot summers.

Fertilizer and lime.

http://www.phgmag.com/garden/desert/200909/overseeding-with-ryegrass/

As devils advocate, I can’t help but wonder why you’d take on lawn work in Phoenix. There are so many spectacular native plants available that won’t endanger your already-threatened water supply.

To say nothing of your energy level on a 120 degree day And your water bill.