Cooking an egg without oil or butter
Well, frying means to cook in oil, so technically you can't. Fat also is delicious, so you'll lose something in the process besides just calories.

If you are using teflon, ceramic, or some other non-stick, don't bring the heat up too much. Scrambling your eggs with milk will make them more fluffy, and I bet less likely to stick. Use (sigh) PAM or another aerosolized cooking spray. Or just 'wipe' the pan with an oiled paper towel. It would impart minimal calories.

It's sad, but microwaving eggs will cook them without adding calories (or anything else). You can also make absolutely delicious eggs by soft-boiling them, which adds nothing at all. 

My more general advice is to learn to love a little fat and to consume a variety of fresh, unprocessed foods which taste great.  It's much healthier in the long run than just cutting away at a number.  Better to go for some walks/runs/lifts then sacrifice flavor.  And fat leads to fullness, which leads to less wasted calories on junk later in the day.