Hey JW, welcome!  I was diagnosed at 27 with type 1 (now 43 but whose counting).  The big "D" diagnosis kinda sends you reeling, doesn't it?  But it can be the beginning of a healthier life, and it sounds like that's just where you're headed.  

Every bit of Joe's advice was great!  I'd suggest you get going first on a walking program if you're not already, then google the "Couch to 5K" program if you find yourself in need of a little structure.  It's a great way to get started running (with run/walk intervals like Joe mentioned) while minimizing the risk of injury and increasing your chances of being a runner for life.  Maybe find a local 5K race that will be towards the end of that program and sign up for it with the goal of completing it. 

I don't know your individual situation with meds, etc.  If you are on insulin, there is a bit of a balancing act to be figured out.  If on fast acting insulin, work with your doctor or educator to figure out how much to either cut back your dose, or to time your exercise to avoid it's peak.  Test before and after you workout (and perhaps during) to get an idea of how your blood sugar is reacting.  As Joe said, ALWAYS make sure you have quick access to some fast acting carbs (glucose tabs, gels, etc.).  Everyone is different, and getting to know your body is the only way. 

But I think the best advice would be to go slow, enjoy the journey, and appreciate running for the pure joy of it.