I'm currently 15 years of age. 5 foot 9 inches and I weigh about 260lbs. My Doctor has told me that I really need to lose weight
Effin lol'd at that, really. I'd have realized that about 100 pounds ago.
Everything that you need to do has been said. Saw some stuff about going pure vegetables, now that's actually bullshit and will make you worse off than you already are.
Everything else though has pretty much been mentioned, mostly. High intensity training is fantastic, but at your current stats it will not help you much as you won't be able to do any of it (say jump rope) without getting hilarious looks from other people. Which in reality is the actual reason you want to loose the weight correct? Cause at 15 years old I'd figure you've still got another 20-25 before your heart shuts down and your pancreas explodes so if you're worried about premature death worry no more, eat all the Big Macs you want and enjoy life.
Again, repeating this all just for posterity. You need to run. 30 minutes of cardio at %80 of your max heart rate is the going number for the most efficient fat burn, but it's also unlikely you will be able to keep that pace up so slow yourself down. Do not walk, it's useless, you need to at least jog. Common misconception, say you run for 10 minutes, you feel tired, and you call it a workout? No, rest, then get back on the treadmill or the pavement.
Your diet probably sucks, but you may feel after a workout you are "allowed" to eat the crap you do now, no again, it's just pushing you further back. You may be tempted to lift weights (understand muscle weighs more than fat so when you are lean enough, hitting the weights will help burn more fat) but if you sit there curling 30 pound dumbbells people will look at you and laugh because with your current situation it will not help.
If you ran everyday you would not see results in a week, a month, or even by the time school starts back up, you'll still be a fat pos. This will take you year(s) to reach a healthy weight. You may loose a few pounds right off the bat but understand that's because you just lost water weight and (should be) starving your fat ass.
Cliffs:
-If you read this entire post you're doing it wrong faggot, you should have stopped at "go run".
-Not sure what shit you're eating now but it's apparent that it's reflected in your appearance. More rice/beans/fruit/complex carbs.
-Results aren't gonna happen overnight, odds are you will become demotivated in a month and give up. Surprise yourself and keep going.