A BMR calculator online said I need 1533 cal/daily to MAINTAIN my weight. How can I lose weight?

I've read that, to lose weight, you should cut 500 cal from your diet. But I've also read that you shouldn't go below 1200/day. Will I burn enough calories exercising to lose weight? If I do a pretty rigorous workout in the eliptical for 30 min I only burn about 300 calories. I have 65% lung capacity.

I'm 19, 5'8" and about 145lbs. I only want to lose about 10lbs, or just get in better shape. I'm fairly active.