I find the best time to take fat burners is in the morning, on an empty stomach as this will help your body target fat storage cells for energy. Also before you workout these are most effective times to use fat burners using the same concept as above the L-Carnitine is responsible for using fat as the energy source of your workout instead of carbohydrates.
These capsules workout well with a healthy balanced diet, as long as you're intaking all the correct nutrients you don't need a special regime.
Just make sure that you are getting the essential proteins for muscle recovery post workouts. If you are training more than five times per week you should have a high level of protein intake which would be 2 grams of protein per KG.
Here's a rough calculation for protein intake.
Workouts per week
5 times per week 2 grams protein per KG bodyweight
3-5 times per week 1.4 grams protein per KG bodyweight
1-2 times per 1 gram protein per KG bodyweight