I think Atkins is pretty simple, and it works if you follow the plan
Eat as much meat and eggs as you need to to feel satisfied, eat 2 cups of salad veggies and 1 cup of acceptable cooked per day (or 3 cups of salad veggies). You can also have up to 4 ounces of cheese, but not cottage cheese, mayo, full fat salad dressing (reduced stuff usually has sugar) just keep your carbs under 20 per day.
Add 5 carbs from the acceptable list for a max of 25 per day. Stay at 25 for a week, then move up to 30 with carbs from the acceptable list. Keep going up 5 carbs at a time, working your way up the carb ladder by adding different foods (they're listed in order in the book). When you quit loosing weight, back up on the carbs if you need to keep on loosing.
Be sure to take a vitamin and a fiber suppliment and keep drinking your water - good job on that so far!
I recommend staying away from processed meats, aspertame, and all sugar alcohols for the first few weeks. If you want to eat them later you can experiment with adding them in and see how you do, but it's important to clear out your system, end cravings, and get the carb tooth under control first.