I used to have the same problem when I first got back into karate (after a ten year break/50 pound weight gain.) I'd be in class for all of 10 minutes, doing drills down the floor... and then the cramps would come! It felt like someone had come by and just whacked me in the back of the calves.
I would of course second what everyone else has said as far as the potassium and the water. For me, a few other things helped.
1.) Weight loss/healthier eating. This one sounds dumb, but as soon as I cleaned up my diet and cut out a lot of the high fat/cholesterol foods I was eating, my symptoms diminished a lot. (Does this sound familiar? Intermittent claudication - Wikipedia, the free encyclopedia
) The reason for the cramp is because your arteries may be a bit clogged. As soon as you exercise and your circulation gets going, the blood SHOOTS down into your legs. Because the arteries are narrowed by the cholesterol, that's why you get the cramp. Maybe.
2.) This will sound crazy but also, worked for me- my karate instructor's secret. When you get the cramp, tilt your head back and pinch your philtrum (the thing between your nostrils.) Breathe normally for about a count of 10... and the pain hopefully will reside. That one worked 9 out of 10 times for me.
3.) Last: time. From my experience, it can take time to develop your "own" running stride. As someone else said, you may be running too much on one part of your foot. When I first started running, I felt like a football linebacker! My relatives are a... hehe, very hearty people. We're all built for strength- what some would call "stocky" and since I've always done burst sports (like karate) and not endurance ones, running was TOUGH for me. I read up a lot on proper running form though and also practiced my form. It gets easier, I promise
Hope this helps!