Here are my 12 Health & Fitness Maxims, ranked in order of importance.  If you want to feel better, lose fat, be healthier, and stronger, I recommend abiding by the following guidelines.  These beliefs are based on Internet research, books, and personal experience only.

1) Calories In vs. Calories Out - If you burn more calories than you eat, you'll lose weight (deficit).  If you eat more calories than you burn, you'll gain weight (surplus).  3500 calories = 1 pound (sort of, of course, tracking calories consumed and burned are estimates too).  Everyone has a base metabolic rate (BMR), which means if you wake up, lie in bed all day, you'll still burn a certain number of calories (organ function, feeding your muscles, etc).  The more muscles you have, the higher your BMR.  Picture two cars sitting at a red light.  One is a 4-cylinder econo-box, the other a V-8 muscle car, both just idling.  You know one is burning more fuel and will need to fill up more often to function.  You can upgrade your body's engine by lifting weights (see #3). 
  You burn additional calories through exercise.  For energy, your body has three sources of food: glycogen (carbs, 1 gram = 4 calories), fats (1 gram = 9 calories), and muscles (protein, 1 gram = 4 calories).  When exercising, your body goes for the carbs first (easiest to convert to energy).  When exercising you have about 75 minutes worth of carb energy before you "hit the wall" (endurance athletes can adapt their bodies to stretch this out to about, maybe up to two hours).  If you are moving slowly enough, based on heart rate, your body burns a combination of fat and carbs.  The problem is, it is difficult/takes time to convert fat into energy (you can improve this as well).  Imagine a rodent in a cage drinking from one of those water bottles with the metal ball.  He only gets one drop at a time.  Your body prefers to store fat if it can (a survival thing). 
  If you are burning too many calories compared to what you're eating, your body will go into starvation mode.  You will have very little energy and your body will consume both fat and muscle.  This is a bad downward spiral.  Because of this, try to lose weight slowly (no more than 1% of your bodyweight per week, and even that's pretty fast).

2) Reduce Chronic Stress in your life - If you don't it will kill you, or make you sick, or encourage you to gain weight, or lower your fertility/testosterone, or up your glucose production (that's nice for the fight or flight thing, but we want to burn fat).  You've heard this before, do what you can.

3) Lift Weights - By lifting weights you break a muscle down (fatigue), it then recovers (#6), adapts (grows in anticipation of having to do that work again and this time it wants to be more capable), and then returns to base/previous state if you stop lifting (use it or lose it).  If you continually fatigue a muscle, allow it to recover and adapt, then fatigue it again (by gradually increasing an exercise's intensity through additional weight, reps, speed or distance) before it goes back to base, it will contine to grow over time.  This is why heavy use of a muscle should be followed by a day or two of rest (i.e., complete whole body lifting exercises MWF or upper body MTh, lower body TuF).  Mild or moderate use of a muscle should have a rest day or two per week (think half marathon training programs).

4) Get Your Sleep - Lack of sleep increases Cortisol aka the stress hormone (#2), you have lower levels of insulin in your blood (insulin pulls fat out of blood, not allowing as much to be stored as fat), you have less willpower (you will eat more food and more bad food), you have less energy (won't workout as much).

5) Triathlon Train - aka Cardio Crosstraining.  I prefer triathlon training because it allows me to workout more than if I just focus on one exercise (i.e., running) because it gives parts of my body a break while others are still working (swimming is mostly upper body, running is mostly lower).  Swimming and biking also put my heart rate in the Maffetone zone more of the time so that I burn fat than when I'm running.  When I train for a half marathon I can only run 4-5x/week.  When I train for a triathlon, I can train 7-10x/week.  But always have a day off every week so you can...

6) Rest/Recovery - Do it.  Exercise should be fun.  If you never give your body a chance to recover, you'll always be sore with pain, you'll be asking for an injury, you'll start to dislike fitness.  Working out puts stress (#2) on your body.  It needs to recover.  Sleep (#3) only gets you so far.

See Part 2 for the other 6 maxims.