When I was in Architecture School, a classmate asked me if I wanted to do some drafting at night and construction during the day. I thought initially that this would not be the best way to spend the summer, but I agreed anyway.
Later that month, not only was I having fun even though it was hard work (a great workout and free dinner/drinks from the boss), but I also learned some useful skills, learned how the other trades solved problems on the spot, and most importantly for me as an aspiring architect, I learned how materials are fastened together which helped me figure out how to draw a good construction detail.
I think it would be a good idea to get your foot in the door by joining a Design Build firm which means this company does both the design and drawings of a house as well as the actual construction of a house. The more you know about construction the easier it is to solve a problem.
You should also take advantage of YouTube to see how a house is constructed from the ground up, go to your local library (or your computer) and read and learn as much as you can: Fine Homebuilding and Journal of Light Construction come to mind. check out Do It Yourself shows. One of my favorites is This Old House.
In addition to working at your construction job, try to find a local Coach or Mentor (an experienced contractor) in the construction industry who you can talk to regularly maybe weekly to help you stay focused. I recommend setting goals with your Coach.
It is possible over the years that you may actually get interested in Architecture and Engineering in addition to Construction. Whatever you do, go in with curiosity and ask plenty of questions. And have fun.