How to study the effect of sustained exercise and sport on well-being? I´d like to make a little case study about the impact of including regular weight training in life. I know one man who is going to start to excercise regularly and I have an opportunity to talk with him regularly (for example every month) for about six months, maybe longer. Is there any other option of making this research than via regular interview with direct questions about his view of the impact of sports in his life (for example question: What do you think you´ve learned from training?)? 
I mean - If I will watch for example self-esteem and it will grow, how can i know it grew thanks to sports and not because of any other change in his life? How to relate any watched cathegory to the regular training?
Just to give you a few ideas. The ideas are ordered from better to worse. They are also mostly ordered from serious and expensive research to less serious and cheap research.

Randomised control trial: 
If you are really interested in causality, you would randomly allocate a large group of people to either and exercise or one or more control conditions (e.g., no exercise; alternative activity; etc.) . You would then use various well-validated measures to measure the dependent variable of interest. For example, if you are interested in self-esteem, then you might get self-report measures using something like the Rosenberg Self-esteem scale. An even better study would measure a range of related dependent variables (reports by others of well-being; physical health; other life outcomes of interest).

It sounds like you are interested in longitudinal trajectories of this effect, so you'd want to measure these outcome variables on multiple occasions (e.g., baseline, 1 month, 2 months, 6 months, etc.).

You'd probably also want to do some kind of intention to treat analysis. Basically, there are two questions. What is the effect of the intervention for those who actually follow the protocol, and what is the effect of the intervention for those who are assigned to it but may or may not actually engage in the exercise?

One sample longitudinal study:
A simpler design would just be the same as above but without the control group. You'd have more threats to causal inference, but nonetheless, results would still be informative to the effect of exercise on self-esteem.

Single participant longitudinal study:
It seems like this is what you are talking about. There are many issues with this design. Do the results generalise to other people? Is the increase due to other factors in the person's life? That said, if this is just for hypothesis generation or exploring the ideas, it might be interesting.

Qualitative versus quantitative measurement:
Quantitative measurement of self-esteem is generally better if you are trying to test formal hypotheses about change. 
Qualitative methods (e.g., asking open ended questions) is often more useful in generating hypotheses and explanations for the obtained results. That said, much more subjectivity can enter interpretation.

As an aside, it is interesting that the vast majority of infomercials selling exercise equipment rely on the cheapest and worst design: qualitative single observation measurement (i.e., anecdotes).