A healthy eating schedule (and healthy foods) is just as important as a healthy amount of exercise.
But 'healthy' is subjective for each person, and everyone should experiment to find what works best for their weight loss.
Healthy and realistic expectations are most important - it is not good to drop all excess weight overnight, but so many people seem to expect this to happen, and often without hard work. Gradual but steady weight loss is the healthiest, and easiest to maintain.
I try to eat mostly of fresh fruits/vegetables, whole grains, aiming for a variety of colours in every meal, and avoid take-away or pre-packaged frozen meals. Slightly higher protein, and lower simple carbs helps me avoid the sweet cravings between meals. However, more important for me is long sessions of endurance-aerobic exercise (long long walks/hikes) and daily stretching. High-impact / fast burn exercises always result in me injuring myself, so I have learned to avoid them. For other people, these exercises may work wonderfully.