Obtain counseling if the person is close to you. For example, if the codependent person is your spouse or grown child, then counseling for both of you will help you to break free of the codependence and the enabling of it. A professional counselor can combat the codependent person's behaviors, while teaching you how to refrain from encouraging the codependency.
Form hobbies and interests separate from the person. If you start to do some things on your own, the person learns to rely a little less on you for her every need. Start simple with, say, a painting class or frequenting your local library. Be firm in doing whatever it is alone, but make it a point to remain consistent in other areas so the person realizes that you continue to return, despite forging your own life.
Communicate about problems that arise in the relationship. Deal with things head-on, and encourage the other person to speak his mind and express his views on the situation. Codependent people tend to stay in the background, never asserting themselves or expressing their feelings. Encourage the person in your life to speak up, talk about what he feels and confront you when you cross a boundary.
Offer reassurance. This shouldn't be in the form of "I will never leave you." This simply isn't realistic. Instead, explain that the person will be okay whether you are there or not. Reinforce her own sense of strength and resilience. Explain that while you are in the picture now and your relationship is solid, she is strong enough to stand on her own whether you are there or not.