It depends on how you mean by "Proper". To me, the proper way to run is in a way that prevents injury so you can enjoy running for either long durations of time and/or uninterrupted calendar periods due to injury. Some may subscribe to proper meaning achieving the greatest efficiency or pace or otherwise fastest times. My answer/advice to your question focuses on preventing injury, which I believe is the proper way to run.
I've read many articles in print and on line, consulting a coach, and have gone through a lot of trial and error on this subject over the last 15 months. There are wildly varying opinions on this subject.
Some people recommend "barefoot" style running or minimalist style. Others may recommend forefoot, midfoot running. And yet others, usually "traditionalist" Doctors and Scientist seem to support only negative results from anything but a mild heel strike.
My personal experience is that I was always a chronic and severe heel striker. And every year when my mileage and/or intensity picked up, I ended up with the same nagging injuries (chondromalacia, shin splints, etc). Last March, I transitioned (not over night) into a forefoot stride with the help of my coach. I transitioned rather quickly over about 2 weeks, running about 10-15 miles a week and incorporating some running drills. I have been injury free since. Please read this as being the recommended approach for ME and what works for ME.
My advice to you is if you make a change, do it very, very slowly. I transitioned quickly, but I've also read of people who took several months to change their stride.
Also, before you run any more, please, please, please go to a specialized running store. I like Chucks too, but not for running. There's a whole plethora of information on shoe types and topics like pronation that your running store will be able to help you with. Finding the right shoe (or at least a good shoe) is very important.