Every diet seems to come and go as a fad. You try it for a while, it either is obnoxious and you are cheating or you stick to it closely and if it works it is only for a couple of pounds. I found a few years ago that Atkins works well for us.
The basic idea of Atkins is limiting your intake of carbohydrates. There are a whole bunch of books written about Atkins and about low carb diets, but in general what you need to know is available for free on line. You start off with two weeks of extremely limited carbohydrates and slowly can add them back into your diet as long as you continue losing weight (if that is your goal) or aren't gaining weight. Pretty straightforward and doesn't require higher math skills.
In our household we enjoy protein, whether it is from eggs and cheese, or fish, poultry and meat. A diet such as Atkins, then, that has you eating protein is just fine with us. While in the early stages you limit vegetables and fruits, it is a lovely time to have fresh steamed broccoli, olives, artichokes and other relatively low carb offerings. But what is wonderful is that you can have that egg salad without guilt.
One thing we have found with Atkins is that you really do need to consume some carbohydrate to get the optimum effect from it, so going with zero carbs for a day really doesn't help. We also find that when invited to eat out or at a friend's house, there is no reason to broadcast that we are doing Atkins. We weren't even set back with the full Thanksgiving dinner noticeably because we quietly didn't overdo the carbohydrate we consumed too much. So we really enjoyed the turkey, had a little cranberry sauce, a little dressing with a nice puddle of gravy, a little of the sweet potato casserole, a lot of the Brussels sprouts swimming in butter and cheese, and a small slice of pumpkin pie. Our hostess had no clue we were dieting. Over the next few days our weights continued to drop.
We don't buy special low carb prepared foods for Atkins, we rather visit the meat department, the deli and the dairy department of the grocery store. I don't attempt to do special Atkins recipes but use the simple broil, bake and sautee recipes we enjoyed during non-dieting times. I just select recipes that don't call for pasta, flour, sugar or high carb sauces.
These days I am still 40 pounds below where I originally began Atkins five years ago and my husband is still about 50 pounds below where he started. It is easy enough when one of us has begun putting on some weight to just slide back into the low carb lifestyle for a while to take it back off.
The only problem that I have experienced with Atkins is that when your weight plateau you need to watch your cholesterol levels. The diet does not seem to be a problem with cholesterol levels until you plateau. And at that point it is time to do exercise with a more low cholesterol version (lots of poultry and fish) until you are back on track again.