First off be very weary of personal trainers. 99% of them really don't have a clue what they're talking about.
The most efficient way to burn fat cardio wise is to do High Intensity Interval Training (
HIIT). This translates into something like this, 60 seconds jog then 30 seconds sprint and repeat it 5-7 times. When you can sprint at full capacity for the 7th set then increase the sprint to 45 seconds. This can also be done in a pool. Stay away from usine a stationary bike. Its not completely useless but there are many better pieces of equipment to use. If you can sprint on a track of some sort. You're build up much more leg strength on a track than you wuld on a treadmill.
Do it AFTER you're weight training. It's more important that you're completly ready to move weights than it is to move your legs and arms back and forth. Nothing worse than being fatigued benching 250lbs and not using correct form because your body is fatigued from cardio. Thats a recipe for injury.
Do
HIIT 2-3 times a week. Lower your carb intake to just low glycemic carbs (veggies, oatmeal etc.) except post workout when you should take in high glycemic carbs and protein. Break your meals into Protein + Carbs Meals and Protein + Healthy Fats meals. And take a multivitamin if youre not taking one now.
HIIT plus intense weight training and a dialed in diet will have you dropping fat like crazy AND IN A HEALTHY MORE EFFICIENT WAY!