Deciding to move is never easy. However, deciding to move to another state while leaving your parents behind is an even bigger challenge. Discussing the situation with them openly and honestly is the only way to handle it respectfully.
Preparation
Create a list of positive reasons for the move. Even if you don't actually refer to the list during the discussion, it's good to clarify your reasons.
Plan the move. Develop a detailed plan for after the move so that your parents will know that you've planned ahead. Plan how you'll find a job, a home and transportation as well as making a timeline for the move.
Realize what kind of help you will need. Think about whether you're expecting your parents to help you in any way, such as storing stuff for you or giving you a ride to the airport. Write a list so that you don't forget anything.
Communication
Find quality time with your parents. Choose a time when no one needs to be rushing out the door or is otherwise occupied.
Start by appreciating all they've done for you.
Explain all the good reasons you need to move.
Tell them that you're moving. Unless you're a minor or need a lot of financial help for the move, you don't need their permission. You do, however, want their blessing.
Allow them to ask you questions. Remember that they're not attacking you; they're just worried and will miss you very much. Try to answer them honestly.
Ask them for what you'll need from them. Make sure to send them thank you cards for their help.