1. Prep yourself mentally.
Create a powerful and affirmative goal statement. Example: "I am so happy that I look and feel great because I have lost 15 pounds of body fat in a fast, healthy way!").
Write your goal statement down on some index cards and be sure to carry one with you everywhere you go. Read it out loud at least twice per day: once in the morning and once at night. Do this for at least 21 days straight and you'll be amazed at how well it helps you create laser-like focus for losing fat fast!
2. Start eating like a caveman.
There are certain foods our bodies absolutely thrive on. They are the foods humans ate for hundreds of thousands of years before the introduction into our diet of large amounts of processed grains, sugars, and "bad" fats, which occurred over just the past few hundred years (the blink of an eye in evolutionary terms).
Base your diet on these healthy, natural foods: lean meats, fish, eggs, vegetables, fruits, nuts and seeds, and healthy fats from olive oil, nut butters, avocado, etc. You can also include large amounts of beans and legumes if you wish -- though they aren't considered to be "paleo" foods -- because they contain the kind of fiber-rich and nutrient-rich "good" carbohydrates that can assist greatly in losing 15 pounds fast.
3. Do short, intense, "interval" workouts 3-5 times per week.
Exercise is vital for burning fat and getting rid of pounds quickly. The best type of exercise for losing weight fast involves doing short bursts of high-intensity activity followed by brief periods of active recovery. This is called interval training and it works both for strength workouts (e.g. circuit training and CrossFit style workouts) and cardio exercise (as in the case of HIIT workouts).
That's it! Do the above things on a regular basis while being sure to get plenty of rest and recovery (at least 7-8 hours of sleep per night) and you will lose 15 pounds fast. You might also want to give yourself a "cheat" day where you can pretty much eat anything you want (this only works if you eat a very strict diet during the week!).