You aren't going to lose a lot of weight just by cutting calories, but its probably a more sound way of going about it.
The math breaks down to this.
1 pound of fat = 3500 calories/7 days = 500 calories a day
If you cut back 500 calories a day from your regular eating habits, you'll lose 1 lb without doing any excercise, because your body will need to burn the fat stored in your body instead of the extra 500 calories its used to.
Most people are eating closer to 2500 calories a day than the recomended 2000, so if you were to follow the 2000 calorie rule, you'd lose a 1lb a week without any extra exercise. Not a whole lot, but the general concensus is that the faster you lose weight, the more likely you are to gain weight unless you make serious adjustments to your lifestyle. The only drawback is that eventually your metabolism corrects itself and you won't continue to see the weight loss happening without exercise, but its a good way to get started and lose a few pounds which is good motivation, and as long as you continue to stick to 2000 calories, you probably wont see any of the weight come back.
The best way I can say to cut out 500 calories is to switch to diet soda from regular. Consiuder that 1 can of soda has about 40 grams of carbs (x 4 calories per gram = 160 calories) in it, and you get the picture. This is why you don't necessarily need to go strict Adkins/Low Carb diet to get the benefits of it, just cut back on unnecessary carbs like in candy and soda. I could never do those diets because I love to eat pasta and rice, but pasta and rice are much better for you in their equal amount of carbs than a soda or a candy bar.
I was so close to going for a Bachelors degree in Nutrition instead of qutting Culinary Arts school after 2 years, but my scholarship was only for 2 years and I couldn't afford the extra 2 years.