So first of all here is my stats. I'm 5'7 and seventeen years old, I weigh about 209lbs since my last weigh in, and my bmr is 1819 calories. I try to eat close to that but I work out so intensely that I can burn about 1,000 calories a day if i do two work outs. And by then my net calories are only like 800 something. I try to eat them back but its too much food, but when I go to bed I'm hungry as heck. I started to feel very tired as well which I began to think was because I wasn't eating enough and noticed when I took a day off I felt a lot better. But my weight has been stuck between 209-212. I don't know what I'm doing wrong, should I cut down on such vigorous exercise so much and just do one until I can get the hang of my eating? And will bringing my calories up promote further weight loss? I do notice that when I bring them up occasionally for a day my scale will go down to 209.6 but then I exercise and I'm back at 210.8 or 211[The next morning, I only started weighing myself everyday because i noticed this problem.] It's just confusing and frustrating for me. I think I'm a bit of an exercise freak but i can't eat enough to back that lifestyle up yet...so I'm basically lost... and since the beginning of January I've only lost 2lbs. Which is pretty sad considering I wanted to be under 200 by February..
Yes, you need to eat more. Right now you're depriving your body of the nutrients and energy it needs, so naturally, you feel exhausted. Here's a post I wrote about why it's important not to eat under your BMR -- you might want to read that first. And here's a post to someone else that was undereating, with a simple explanation of the math.
Your actual numbers will be different because you are taller, younger and heavier. You're close to the border of teen/adult, so you might want a different calculator to find your BMR and your daily calorie expenditure. When I run your stats with an average mid-year birthday, they show me a BMR of 1800 and a total sedentary burn of 2280.
Sedentary burn is, for you, BMR + almost 500. So if you eat at only your BMR (1800) without exercising, you are already at a deficit of 500 per day. You can lose weight that way; it's enough for 1 lb per week.
But, you are willingly burning 500 to 1000 calories MORE than sedentary level, by exercising. On that calculator, "Low (light) activity" is 470 calories more than sedentary, so it's just about the same as a day with one exercise session: sedentary burn + 500, or BMR + 1000. With this level of activity, you'd have to eat 2800 calories to maintain your weight. "Moderate activity" is 920 more than sedentary, almost the same as burning 1000 calories with exercise (or two sessions in one day). So you can see very clearly there: To maintain your weight while burning 1000 calories with exercise, it would take 3300 calories per day.
So, now about deficits: taking in less energy/calories than you spend. A 500-calorie deficit per day equals 3500 calories in a week, or one pound. A 1000-calorie deficit per day = 7000 = 2 lbs per week.
The recommended amount to lose is 1% of your body weight per week. At your current weight, that allows you 2 lbs per week. The reason it's recommended is that the body has trouble metabolizing fat at rates higher than basically 1% of bodyweight per week. At a deficit higher than 1000, you'd be losing more weight than 1% and start losing muscle and lean body mass instead of fat. So your deficit should really stick around 1000/day max. In other words: [total daily burn] -  = calories to eat... with a condition or two.
It effectively means that on days when you burn 1000 calories with exercise, with a total burn of 3300 for the day, you need to be eating at least 2300 calories. On days when you burn 500 calories with exercise, you're spending 2800 above maintenance and should eat (at least) 1800. However, a lot of people find it easier to lose weight while eating more than the bare minimum. And this probably has something to do with the BMR.
On sedentary/rest days, you can just eat 1800 (your BMR). You'll still have a deficit of 500 and will lose weight. But, you'll have no calories to spare for exercise, because that 1800 is dedicated to body maintenance and function. Think of it like a "low idle". Your body's not using much fuel, but it doesn't have the energy to do much, either. If you work out and burn 500 calories while eating 1800, you've just reduced net calories down to 1300, and your body can't maintain itself on that (so if you keep doing that, it will adjust and you'll probably have poor results). If you choose to stay at 1800 calories a day, you really must eat enough food to counterbalance whatever exercise you do.
In fact, since you like exercise so much, you could just choose to eat at maintenance (2300) every day that you exercise normally. If you burn 500 you'll bring your net calories back down to 1800, so you're below maintenance, but without cutting into your BMR (no "starvation mode"); plus the exercise will kick your metabolism up a notch and you'll have more energy. On days with more than one exercise session, you'll want to eat more to match that expenditure, and on rest days you'll want to eat less to avoid over-splurging. So: rest day = 1800 (or more if you prefer), exercise day = 2300, double exercise day = 2800.
Note that the precise numbers aren't the point, but the pattern of eating to compensate for how much energy you burn is the point. Track your individual workouts on here and use those calorie estimations to adjust your eating. I bet you'll get the hang of it pretty quick -- eventually, you may even just listen to your body, notice hunger signals and meet them. (though probably not until you are satisfied with your weight and willing to relax :P)
Right now you just aren't getting enough nutrients for your body to let go of the weight. But your body already is responding well when you eat more; I imagine you'll see very nice results once you start meeting your optimum calories.
Also -- I love exercise too, but please, please be careful and don't let it become compulsive. All these lifestyle changes are to help your body work better and basically make it happier, right? But over-exertion and under-eating are starvation to the body, and we just don't thrive under starvation conditions. Plus, it really sucks to become obsessed...
As far as functionally being able to eat enough to meet your calorie goal: it's a balance of eating frequently enough, having enough food at once, and choosing healthy yet calorie-dense foods. Count on 3 or 4 meals, and at least 2 or 3 snacks a day. Meat, cheese, nuts and nut butters, fruit (fresh or dried), avocados, whole eggs (you can take hardboiled eggs with you for a snack)... If you're vegetarian or vegan, add in more dairy or soy products and beans. Try to incorporate the extra food into your daily meals, but be sure to keep 'emergency' rations on hand in case you don't have enough calories at the end of the day. (Peanut butter sandwiches are an easy 400 calories.)
Be sure you are actually measuring your food, especially high-calorie items. Use measuring spoons, cups, or a food scale if you have one. It's hard to track your calories accurately if you don't know exactly how much you're eating, and training yourself to recognize portions is useful no matter what your weight. Most people worry about over-eating -- but it sounds like you need to worry about under-eating.
Keep in mind that vegetables, usually moreso than fruits, are bulky and filling without providing much in the way of calories. Vitamins and nutrients are important, but if you can't eat much food at once, it's really important to work on getting the calories in first. As you get accustomed to eating enough, it will be easier to adjust the exact ratios of different foods and nutrients :)
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