Water is usually the biggest problem that needs to be solved to develop the best looking lawns. Lawns need from one inch to one and a half inches a week. If the soil is good and of adequate depth it is best to apply water twice a week. More water than 1.5 inches will weaken the root system because it slows the movement of oxygen in to the soil and the root require oxygen to survive. When less than an inch of water is applied the soil will dry out between water and the top of the grass will start to go dormant.The amount of Fertilizer the grass needs depends on how is it used and what you want it to look like, here is a good article on the issue.
The article focused on nitrogen because it is the nutrient the grass needs us to supply the most, the other nutrients you may need to supply are phosphorus and potassium. A soil test will help you determine how much, if any, of these nutrients you need to apply.
