I found that running minimalist/barefoot corrected my running form pretty quickly and naturally without any special effort on my part.
You body just won't let you slam your heel into the ground like you can when you're wearing regular shoes. If you do, you'll feel the bone-jolt all the way up your body and it will shake your fillings loose!
Also, running minimalist/barefoot makes you land your foot softer almost intuitively. You frequently read about 'running soft' as a form goal and minimalist/barefoot running seems to help with that.
It takes a bit of time before all the sissy-weak-shoe-atrophied-muscles (yes, that's a real word!) strengthen, but once they do you'll be amazed at how many muscles you weren't using before when your feet were trapped in laced-up foot coffins.
Although not directly related to your question on running form, I would suggest that the next step after minimalist running shoes is some kind of ultra-minimalist footwear. Two of my favorites are a $6 pair of water socks from Walmart and huarache sandals with a 4mm sole. It feels fantastic when the wind blows across your bare foot. In the winter I usually run in the water socks with an additional pair of cotton socks on my feet.
After all the muscles in your feet and legs have strengthened, then you'll be in better shape for the final push to barefoot, where all you'll have to worry about is toughening up the bottoms of your feet.
To do that, pop the footwear off near the end of a run and run the rest barefoot. Or pop the footwear off after the run and walk barefoot during your cooldown walk. Just take it easy because asphalt/concrete can blister you up pretty quickly until your feet toughen up.