Change your Identity. If you've been in a dependent position for a long time, chances are that dependency has become ingrained into your identity; your vision of yourself; your self-concept. You may even engage in labeling yourself, "I'm a dependent sort of person" (labeling being a cognitive bias you might want to look into correcting).
To the extent that you see yourself as a fundamentally dependent person, you might profitably spend some time exploring how this identity came to be, and whether it fits who you want to become. The effort you put into exploring the reasons and ways you have come to think of yourself as fundamentally dependent will pay off by increasing your awareness and insight, which will, in turn, help you recognize and correct your dependent beliefs and behaviors.
Attend to the Past. List out the events and occurrences in your personal and/or family history that have led you to a place where you feel that you are a dependent person. Is there a legitimate alternative way to reinterpret (reappraise) these events that casts you in a better light? Can you allow for the possibility that your situation can change over time as you mature and new events occur? Examining how you came to believe you are (or must be) a dependent person may help you understand the motivations you have for continuing to believe this to be true.
As an illustration, imagine that your spent your young adulthood with a depressive mother who leaned on you heavily (perhaps too heavily) for support. In the emotion of that time, you may have formed a belief that you must defend and support your mother at all costs. Another belief may exist as well to the effect that your mother cannot survive emotionally without your support. Such beliefs create a strong sense of duty and responsibility inside you, and a strong sense that you must never be selfish with regards to your mother, even if what she asks is out of line. These forces could be expected to sustain within you a strong dependence on your mother. In order to start taking that dependence apart, it will be helpful for you to examine whether or not it was fair of your mother to have asked you to support her in such a manner, and whether your early assumption that you are responsible for your mother's happiness is in fact reasonable. If you can see that it is, in fact, unreasonable for you to think that you can or should be responsible for your mother's happiness, then you are less likely to act dependent upon her.
In the process of breaking free of overgeneralized duties and responsibilities from your past, you may have to deal with feeling guilty for asserting your own needs over the needs of others. Such guilt is a product of a misunderstanding, on your part, and perhaps on the part of your relationship partner; a product of broken or misconfigured boundaries that you would do well to repair and rebuild. It is perfectly okay to assert your own needs, so long as you do not go too far in the selfish direction and lose all empathy for others.
Attend to the Present, and to the Future. When you are done looking towards the past to see where your dependent identity came from, consider examining your values to see what your dependent identity might transform into. Your values are what power and motivate you to change. The more you become conscious and aware of ways that your present day beliefs and behaviors fail to fit with your values, the more you will have energy to correct those beliefs and behaviors so as to better shape them towards independently chosen directions.
"The journey of a thousand miles starts with a single step", as the saying goes. Remember that it took you some time to become a "dependent" person. It will similarly take some time for you to grow to become a more independent person. Allow that to be the case and just focus yourself on each small step in the process of change, one step at a time. There is no hurry. Changes will occur gradually; not all at once. There may be setbacks and relapses, all of which are okay so long as you do not use them as an excuse to give up your self-help efforts. Instead, when you fall down, dust yourself off, rest a bit and then pick yourself back up. The more you practice independent and assertive behaviors and thoughts, the easier it will become to keep doing so.