Is there a scientific way to go about self-improvement? I know it starts with determining the "need" for improvement. But what does one do after that? How do you assess the various ways you can go about self-improvement?

Think about it- use the scientific method if you wish to be scientific. Ok, so most of the experience will be subjective, and I do suggest sticking with 'what feels good,' etc, but there are 'objective' analyses one can make. Keep track of weight loss or gain, skin tone, energy level (not objective enough? Just measure how long you slept and how long you stayed awake and functional with and without certain methods.)
Another good thing would be to look for studies that have been verified by multiple sources. While this is not empirical evidence of the truth or falsehood of any particular method, it does give subjective-type evidence for the different methods. And of course, you can study these methods on your own as well. Keeping a journal or logbook with recorded changes in health (incidents of sickness, general well being, energy, appearance, whatever) can be usefull as well- in fact almost necessary if you wish to test something, as it extends over a period of time and can be filled with tabled measurements which can help explain the hypothesis.

Oh! I almost forgot one of my most important suggestions- there are lots of tests available, even online, which are usefull for measuring self improvement-iq tests, eq tests(not sure whether these are garbage or not, but the one I did seemed to have a few flaws. Nevertheless, they are fun to do), health assessments, exercise standards, health guidelines, what have you.