If you are the type of person that has the "I can fix anything attitude" than you are on the right track to becoming a Handyman. Not anyone can become a handyman, to do so you must have good hand and eye coordination because a lot of tasks you will be doing around the house will require this. Say for example you are soldering a copper to copper this will require steady hand movement to keep the flame just the right distance from the point you are soldering together.
Basically the more you do a certain thing or task the better you get at it. The more mistakes you make the more you learn from your mistakes, like I have changed out a couple hundred tub stems and I have made mostly every mistake you could possibly make doing so, but I have learned and my hands on experience has taught me what to do and what not to do.
See I am currently working at an old apartment complex, and at this old apartment complex with over 500 units guess what, everything breaks, there is always something to fix, somebody is always calling a problem in, when that happens me or another one of my co-workers go and fix the problem. I have been working at this old apartment complex for a couple years, and to think that I do about 20 service requests a day, mostly all of them are different. This is the best way to learn, being a multi service tech that is constantly troubleshooting and making repairs on HVAC systems, plumbing leaks, electrical issues, drywall, appliances, carpentry, and many other things. But once you fix a certain problem so many times you become an expert at it. You could read every book in the world on HVAC trouble shooting, and after you do I would like to see you trouble shoot a faulty A/C system. Without hands on experience you aren't going to be able to fix shit. So if you want to become a jack of all trades all powerful handyman, and your willing to put time into learning become a maintenance technician at a crappy apartment complex that is old and run down, this will give you the experience that you need to become a successful handyman.