Keep your net carbs (carbs minus fibre) at around 20-25, and get around 80 grams of protein in a day and lift weights. That is the fastest way to lose weight (keep your overall calories to around 800-1200). Focus more on weights than cardio. 20 minutes of weight lifting may burn less total calories during the workout than 20 minutes of cardio, but you will burn more calories for the entire rest of the day plus while sleeping as lifting weights really ups your metabolism (and helps you maintain the weight loss once you're at goal).
Yes, HITT is very good for fast weight loss, esp if it's 30 seconds - 2 minutes high intensity cardio, then lift heavy weights for 5 minutes or so, for a total exercise session of 20-30 minutes. If you can do more than that, it wasn't intense enough. The 30-Day DVD by Jillian Michaels is a great example of this and you can watch online for free. A pure Cardio HITT is also good (2 min walk, 30 second sprints) but not as effective as switching back and forth between cardio and weights.