It's pretty late to seed and hope for it to last the summer. But you probably don't have a choice.

Get the seed down as soon as possible. Water it 3 times a day for the next three weeks, then cut back to twice a day for a week, then you'll probably need to water it daily to get it through the summer.

Next year, water when the grass shows signs of stress, and water deeply when you water. You should be able to get by watering once or twice a week. Watering daily (or several times a day) is common around here, but many of the lawn problems people have are a direct result of too much water (even though it's a desert).

Watering deeply and infrequently helps the grass develop deep roots and inhibits weed germination.

Don't fertilize at all now. The soil around here is rich in P and K, so you don't need a starter fertilizer and you don't want to encourage fast growth this summer at the expense of root growth. Once it cools off, use some ammonium sulfate (21-0-0 or urea (46-0-0) and spread it so that you get about 1 lb of N per 1000 sq ft (about 5 lbs of the 21-0-0 or 2 lbs of the 46-0-0 per 1000 sq ft). Fertilize twice this fall, once shortly after the heat of summer breaks and once after the top growth has stopped but while the grass is still green. That will help it green up faster in the spring (and it may even stay green under the snow all winter) and will help it to develop strong roots.

Thanks bpgreen. How long should I be watering the lawn for the 3 times a day now? What times are best to water?

You basically want to water long enough to get the top 1/2 inch or so damp. I'd probably water around 10 AM, 2 PM and 6 PM, but those are really just guesses. The length of time to water depends on your sprinkler system, but 5-10 minutes is probably about right.