I think there are so many different diets out there because what works for me may not work for you.
To answer your "how fast" question, I can lose 1.5lb a day by totally stopping carbs. Baked chicken every meal is not exciting but it works. However, true health is a lifestyle and not a cycle. Once you lose weight you can increase your intake but you can't go back to eating poison foods and stay healthy.
For me, I eat paleo. And I should mention that I'm way too old and cynical to even say Paleo, South Beach, etc with a straight face normally. But I eat a low carb paleo diet and can eat whatever the fuck I want, as much of it as I want, and lose weight. I do work out about 45 mins a day as well doing high intensity interval training. This works great for me and at 50, I still eat what I want as long as it is low carb and high protein. You really can't eat enough baked chicken breast to get fat.
#1 rule - stop drinking soda and other sweetened beverages. Just that will work for 90% of the people wanting to lose some weight. That shit should be sold behind the cigarettes at the store. It's fucking poison.
#2 rule - stop thinking of meals as treats or rewards. Meals need to sustain you, not be delicious. You should be as excited about your next meal as you are your next shit, because that's all it is - a required function for your body.
Every week I eat whatever I want (except soda) for one meal. It's impossible to undo 167 hours of proper eating in one hour, and this is the meal I use when I have to go out with friends to celebrate or something. So I still get pizza, just not every meal anymore lol.
Without knowing you I'd say to meet your goal quickly cut out carbs and start the C25K program along with some weightlifting done for cardio (as in lighter faster more reps). You could realistically lose 20 lbs a month or more safely this way.