The double chin can be an absolute nightmare to get rid of. I hate to start with bad news but I have to start with the truth. The good news is that it is possible, it just takes time. The other bad news is that this is a really long post!
First things first:
Get your diet right! Getting rid of a double chin is like getting your abs to show. 90% of it happens in the kitchen. Cut out the processed food, sugars, and any and every simple carb. Most of your diet should consist of unprocessed meats, whole uncooked veggies, and black, brown, or wild rice as the only other carb.
Take fish oil. It actually helps burn fat, especially when taken in the morning. I take 3 grams 3 times a day for a total of 9 grams daily.
Drink plenty of water. Make sure its enough. If you are working out and you better be, I look at a gallon a day to be about right.
Get the proper workout. Cardio helps but can only take you so far. Fat retention is partly due to hormone levels. Big complex lifts boost testosterone and other pro-growth hormones. The higher the testosterone, the less propensity the body has to store fat. Do squats! Do deadlifts! Overhead Press and Bench Press. BIG COMPLEX LIFTS. The last two will really help!
Specific Exercises: The muscles you want to target are the platysma muscles. They are difficult to work by themselves so you really have to work the whole neck. Check out this link for some exercises: Bodybuilding.com Neck Exercises
Bigger traps stretch these muscles wider and will also help so Shrugs and other trap exercises can be useful.
Keep your expectation in check. It takes time! Don't push too hard to fast with your neck man, it's kind of important to have. And remember, even Bane(Tom Hardy) had a little double chin in the new movie.