If you have a valid license from one state, you may use it in other states that you visit. But, if you make a permanent move to another state, you'll have to take a trip to the local department of motor vehicles to apply for a new license. Usually, you must do this within 30 days after moving to the new state. Most states will issue your new license without requiring tests, though some may ask you to take a vision test and a written exam covering basic driving rules.
In some situations, you may be unsure as to whether you need to apply for a new license. If you make frequent business trips to another state, or even if you attend school in a state away from home, there's no need to get another driver's license. But, when you set up housekeeping in the new state and pay taxes there as well, it's time to apply.