It sounds like your lawn is in need of reseeding. The best time to do this is in the spring, though you can do it in the summer too. The first thing do do is to figure out what kind of lawn you have. (Bring a patch to the store; they can tell you what it is.) Then, clear away any dead leaves or grass around your bald spots and sprinkle the seeds over them. You don't need to bury the seeds, but step on the area to make sure they stick to the ground. Water frequently and you should be good to go. Look into lawn fertilizer for the brown bits. And you may want to up the amount of water you are giving the grass.

First you need to determine why it is dying. Is it dry, drought burnt or do you have an insect problem. I lost a large portion of my lawn to cut worms last year. They are infesting large areas in the midwest and west. Once I killed them I am now trying to reseed the lawn. But in Colorado we had a brutal winter, so the entire lawn suffered this winter.