You're right that diet is the major factor - any amount of exercise can be out-eaten in literally seconds. So if you want to manage your body fat through exercise, the key thing is to do the workouts but don't then go and undo it with fizzy drinks or sweet food etc. And that's hard!
I would suggest as much aerobic exercise as your schedule will reasonably allow. That could typically be walking, swimming, cycling or - and I guess this is relevant since you're in this thread - running. Most should be done in the aerobic zones, i.e. a slow pace where you don't get out of breath and you can easily maintain a conversation (this is a commonly-used barometer). This is the most effective way of consistently burning fat through exercise. You can double the rate at which fat is burnt by running fasted, which for most people means before breakfast.
You could incorporate some high-intensity interval training (HIIT) which - in part - works on the principle of raising your metabolism for several hours so you continue to burn calories post-exercise. According to research, the ideal is to go more or less flat out for four minutes, jog to recover, then repeat for a total of four lots. Runners would typically build up by doing a higher number of shorter repeats until they are ready for 4 x 4 minutes. HIIT/interval sessions - when done correctly - are likely to affect training on subsequent days. They also heighten risk of burnout and injury so are only done weekly at most (I'm an experienced runner and I'm doing it once every nine days or thereabouts). I've seen people trying to do them more frequently in an attempt to lose weight fast but it I've never, ever seen anyone able to sustain it; it always ends badly.