What follows is the modified scientific method for the study of the self.
1.Recognizing a Problem
2.Perform some research/Form a hypothesis
3.Design exercises, or play with exercises you found
4.Pay close attention to the subjective results you get (use a journal)
5.Form working conclusions and continue experimentation

Step 1 does not really require a problem, just something you would like to change or improve. Mindfulness is your best friend here. If you want to work on the self or explore the self, it helps to have an awareness of the components of self first. If you have never taken the time to pay close attention to your 5 primary senses or your thinking senses of internal pictures or internal sounds, now is the time to start.

Step 2 suggests that you research the area a bit before formulating your own hypothesis. You don't have to make your hypothesis based on this research, but it helps to know what other people who have worked the field have come up with thus far.

Step 3 encourages us to really get to work. This is where we allot time for meditation or other exercises and follow through. This is where we actually run the experiment, and the experimentation never truly ends. It might change direction, but it will continue.

Step 4 reminds us to track our results. Write down detailed descriptions of your subjective experience as you go. This gives points of reference for the changes you have experienced. When looking through the eyes of the new you, it might not be easy to see how much different you are now from the way you used to be.

Step 5 allows us to put working principles in place to help us continue with further experimentation. Keep in mind, these are just working theories; they are subject to change and improvement.

To illustrate, allow me to share an example from my own life. Several years back, when I was still in the Army, I started meditating every day before I went to work. As I continued practicing, the meditations grew deeper, and it made the early part of the day more pleasant at work. I noticed, however, that I wasn't really developing the ability to deal with my day-to-day challenges in a 'meditative' way (step 1). It was like a peak experience that would wear off. I read through some of the meditation books I had at the time, but did not find anything that really applied to what I was experiencing (step 2). I figured if I could find a way to practice in the morning or throughout the day, I could experience more freedom when challenges come up. So I started playing with quick methods of meditating, and short meditative exercises (step 3). I wasn't very good at keeping a journal at the time, but I did measure my satisfaction with the day, as well as individual experiences with and without applying the techniques (step 4). Based off this, I continued to test and practice these methods to this day. A vastly simplified version of my results would be "When I'm in a good space, I get better results. When I'm in a bad space, I get worse results."

This is only one example, but you can apply this method virtually anywhere in your life. When you do, you will get powerful, measurable results!