Your BMR (Basal Metabolic Rate) is the amount of energy your body needs to function. We use about 60% of the calories we consume each day for basic bodily functions such as breathing, metabolism, etc. Use this formula to calculate how many calories you need to MAINTAIN your current weight.


Women:
655 + (4.3 x weight in pounds) + (4.7 x height in inches) - (4.7 x age in years)

Men:
66 + (6.3 x weight in pounds) + (12.9 x height in inches) - (6.8 x age in years)

An example: Bob is a Male weighing 185 lbs, 72 inches tall, 25 years old.
66+ (6.3 x 185lbs) + (12.9 x 72inches) -(6.8 x 25 years of age) = 66 + 1165.5 + 928.8 - 170 = 1990.3 calories to maintain that current weight

Depending on how fast you want to lose weight, you need to choose how big of a deficit you want to make in your diet per day. Keep in mind, subtracting too many calories from your diet may cause harm to you. Anything more than 500 calories less than your BMR is probably unhealthy.

Bob decides to subtract 500 calories from his BMR so he will eat about 1490 calories per day (1990-500=1490 calories)

So if you decide that you want to do some extreme weight loss and make a deficit of 500 calories per day in your diet, you should lose 1 pound of fat (-3500 calories) per week  (-500 calories X 7 days).

Keep in mind that 1 pound of fat has water and other substances associated with it, so your actual weight may drop by more than 1 pound. It might be more like 2-3 pounds a week. 

Bob needs to lose about 3 pounds of fat, so without exercise this should take about three weeks (-3500 calories per week which equals -1lb of FAT per week)

Since Bob's limit is 1490 calories per day, he needs to decide how he is going to split up his food portions to stay within those limits.

Make sure you have three bigger meals:
-Breakfast: Helps kick start your metabolism from the moment you wake up
-Lunch: Biggest meal of the day, will provide you will energy to do your daily tasks.
-Dinner: Take it easy on your dinner

Two to three smaller meals:
-Small snacks in between each of your bigger meals keep your metabolism working fast

Bigger meals should have more calories
Smaller meals (snacks) should have less calories

Bob chooses:
Breakfast: 300 calories
Snack #1: 150
Lunch: 400 calories
Snack #2: 150
Dinner: 400 calories
Snack #3: 100

Total calories = about  1450 which is PERFECT because it is under our 1490 calorie limit.

Breakfast: Try to eat something with protein because it will help boost your metabolism
Snack: peanuts or greek yogurt are awesome
Lunch: biggest meal, choose anything, just make sure that you stay within your limits
Snack: Anything as long as you stay within your limit
Dinner: Take it easy during dinner, try to eat lean
Snack: Anything as long as you stay within your limit.

Obviously, if you want the best results you should totally exercise. Especially if your really overweight, exercise will definitely help kick start your metabolism. Resistance training has tons of benefits for both males/females. It is shown to boost metabolism, mood, and lean body mass.

If you do decide to add exercise, you can keep track of how many calories you are burning with a heart rate monitor. 

So if Bob decides to exercise 3x a week for an hour and he burns 400 calories every time he works out. That is 1200 calories a week in addition to the 3,500 calorie deficit that we already made! In total, he will be losing (1200+3500) 4700 calories per week, which is about a pound and a half of fat. Or Bob can squeeze in a small desert once a week to since he has some calories to spare. As long as your making a deficit every day, you should be losing weight.