I dont think gym class ever taught proper running form :-p
I googled it and came up with some ideas -
I never really thought about form/posture until I start running around 2-3 miles and I noticed my back and neck/shoulders ached at the end of the run, and then I realized I was running slumped over, so now every once in a while I just pay attention. I think your body will tell you (ie pain/soreness/aches) if something needs to be adjusted.
Congrats on getting started - I was always overweight/obese as a kid and missed out on all the physical activities, so now I really enjoy it.