Exercise is important for a healthy lifestyle, but it won't result in weight loss. The amount of calories burned are trivial.
For example:
- 30 minute run burns (150 pound individual) burns just 272 calories.
- 30 minute lap swim (150 pound individual) burns, again, just 272 calories.
A single Milky Way chocolate bar has 240 calories. A Big Mac has 530 calories. A McDonalds Chicken Classic Sandwich 350 calories. And so on. So you can exercise for an hour and then regain the weight in under a minute. That's how few calories exercise burns.
The primary way people lose weight is BMR (basal metabolic rate), this is calories burned just keeping you alive. You literally lose weight while you sleep due to BMR.
People often like to claim "'calories in' need to be lower than 'calories out'" and while that is true to a point, it is an over simplification (i.e. even with identical calories certain things, like sugar, are kept as fat to a greater extent than other things, such as fiber, which are "ejected").
So, yes, please exercise. You'll live longer, feel healthier, and it might even shed one or two pounds if you're already skinny. But if you're obese and need to shed 10+ pounds then your diet is the primary means by which you'll accomplish your goals, in fact you can lose all of your weight while in a coma on a hospital bed, so all you need to do is under-eat for your BMR (but consult your doctor, and try to eat a balanced diet).
I recommend using something like MyFitnessPal. It is free. Just set it up, it will track your BMR and what you eat, and as long as you stay in the "green" (below the BMR) you'll eventually lose some weight.
However please keep in mind "water weight" is a legitimate thing. Your body does gain and lose +-5 pounds "randomly" so you shouldn't weigh yourself excessively, you'll just lose motivation. Once a week MAX, every two weeks is better.