Depends on what language,platform(s) you are using. For a web development it's enough of print_r() or var_dump() statements. In my experience of 2.5 years of PHP web development - I have NEVER used debugging facilities- just these statements above. IMHO, if you feel the need of debugging (in a web development) this means that something with your code structure is not right and you need a complete code re-write. Then sit down, and re-think deeply how you can help yourself in the future by changing code architecture now.
About the question part - How and where to put breakpoints or print_r() statements in the code. Well, actually nobody can answer this question - just YOU. Because you are the master of your code and just you know it well (except maybe your colleagues or a project manager). Analyzing code paths is a developer duty and we must perform it well. So get used to it, otherwise it may mean that developer job is not a dream work for you.