Atkin's is stupid. The idea is, it's OK to eat FAT calories because it gets burned right way, it's quick energy, whereas carbs are generally stored & processed for energy later.
If you're trying to lose weight -- that is, get rid of excess fat -- you need to reduce your TOTAL caloric intake. That means reducing fat AND carbs, along with exercising. This whole "eliminate entire group X" is dumb. Mixing it up and moderation are much healthier.
But there are a lot of calories that you can get rid of by reducing carbs. First, NEVER drink soda unless it's diet. 240 calories per serving adds up REALLY fast. Fruit juices are the same way -- tons of sugar carbs there, even in the "no sugar added" kind. Water is the best, but if you need flavor go with diet drinks. Bread, bagels, etc. are all really high in carbs in general, but there ARE low-carb variants, and reducing how much you eat can go a long way. Eat HALF a bagel instead of a whole bagel, for example. Pasta is just really really high in carbs. If you're trying to lose weight, I'd definitely recommend laying off pasta (and rice, for that matter) until you've reached your goal, and then keep the quantities down. It just doesn't provide enough nutritional value to justify the caloric intake when you're trying to lose weight. Potatoes, corn and carrots also have a surprisingly high amount of carbs, so stick to yams and other vegetables & keep the others to a minimum. Red meat is also good to avoid as much as possible. Lots of saturated fats there. Better to eat fish, chicken, and lean pork, and much less beef. Also, apples and oranges are fairly high in sugar carbs, but berries have less. Eat more strawberries, blueberries, raspberries, etc. and fewer apples & oranges during the strict part of your diet.
Finally, eat at least 3 meals a day. Don't save it all up for one big meal -- you need to keep your body's metabolism up, and if you do the one big meal thing, your metabolism will crash afterwards. Evening things out is much better for losing weight.
Here's a typical day for me, when I was on the stricter part of my diet:
Breakfast: Small bowl of Cheerios with skim milk.
Lunch: mixed green salad with balsamic vinaigrette, chicken or fish, lots of vegetables (we have a cafeteria at work). At home I'll often eat a half bagel with sliced tomatoes, cheese, and salad dressing for lunch.
Dinner: Large salad, maybe a half bagel. Mixed berries for dessert -- with cool whip sometimes!
To drink, water or diet soda.
I did that for 2 months & lost 30 pounds. YMMV of course.
Now I tend to include a few more carbs & fat, and my weight has been pretty steady.