First, start by watering properly. Without proper watering, nothing else you do to the grass will make it green.
Next, apply a little fertilizer throughout the summer. Without some nutrients consistently added throughout the growing season, the grass will fade and become less green than it can be. If you are watering and fertilizing properly, the grass will grow.
Third, if the lawn is cut improperly, it will not be as green as it can be. Simply put, mow high and let it lie. Putting these three practices together in the right combination and a green lawn is actually quite easy. But remember, once it gets green, there is a maximum level it will be. Once it's looking good, enjoy it, and don't keep trying to make it greener still. You'll be putting the lawn into a stress condition, which will eventually cause major problems.