The topic of nutrition is a variable one. Depending of course on your sex, body type and goals.
So lets first structure this discussion into two sets of people (we'll breifly discuss the third set at the end)
Those who are looking to LOSE fat:
Losing weight can be as simple as cutting a few hundred calories out of your daily diet with very little required exercise. First, you need to determine how much food your body needs, this can be done by doing whatever you normally do dietarily and physically over the course of two weeks, taking your body weight in the same set of cloths, at the same time and conditions (before or after going to the bathroom/eating dinner etc...) every day, it will of course fluxuate but once you've established what is required to maintain your weight, all you need to do is short your body by ~500 or so calories daily.
This can be accomplished by reducing the amount of consumed food, changing the amount of calories you consume (ala consume different foods), increasing the amount of physical activity, or some combination of the three. The general rule of thumb is for every 3500 calories you are short in your diet you will lose 1lb of fat. YOU DO NOT WANT TO BE MORE THEN 7000 CALORIES SHORT A WEEK UNLESS YOU CONSULT A DOCTOR, AND ARE OTHERWISE HEALTHY!!! Part of losing weight in a healthy manner is not going through periods of extreme starvation and or binging.
Those who are looking to GAIN fitness
This is a bit more complicated of a task, there are 3 important topics should you want to do this. And ladies, don't worry that you'll get "beefy" in all honesty, without performance enhancing drugs, 98% of you just don't have the requisite testosterone levels in your body to produce the type of muscle mass that would make you look less "feminine", and the ones that do, well... I don't think you're too worried about being feminine anyway. Now that I've gotten that out of the way. Let's discuss the 3 points, proper diet, sleep and exercise.
When trying to gain muscle you must get atleast 8 hours of solid sleep, no less, more is good. The bottom line, your muscules need to heal after a taxing workout, and in order to be stronger, you MUST tax your muscules.
Exercise, I am 27 and can honestly tell you that your workout is a huge part of getting stronger, you must push your limits to new heights every time you go to the gym and you must go on a regular basis. Does this mean becoming a gym rat? NOT AT ALL!!! 3 times a week, 45 mins at a time. If you're just starting out or even if you've started recently, one piece of advice I would give anyone, stick to compound exercises, the olympic lifts are amasing in improving your overall body health and strength. Each time you perform an exercise you must add weight, even if in small increments (girls think 2 1/2 to 5lbs, Guys 5-10lbs.) This may sound impossible by I assure you it is not. I started working out in the Beginning of January for the first time in 8 years and I saw gains of 65lbs on my bench press, 130lbs on my squat and deadlift, 40lbs on military press and so on over the course of 3 months. This is much more reasonable then you think, start within your capabilities (not to much weight in the beginning, trust me, may seem easy, but pretty soon you'll be wishing you could take weight off)
And finally to diet, to get stronger you must have a proper mix of carbohydrates, protiens and YES, fats. I use the 35% - 25% - 20% rule, but there are many opinions about this that generally are close to those numbers. The other important aspect is to consume slightly more calories then you currently consume, you muscles will need this additional energy during AND after your workouts (to repair your muscles.) If you have the money, protien shakes are useful and a good supplement if you find you have a hard time consuming the proper amount of protien (75-150 grams a day) as I know I did.
Alright everyone, I think I've had enough for now, any questions, please post them in the comments and I will try an help you individually if I can.
Regards,
Aaron