Most people can improve the quality of the food they eat and lose weight. The first thing to do is switch from soft drinks to water. Soda should be a rare treat once or twice a month, not every day. Avoid fast food and eat home-cooked, well-balance meals focusing on a variety of vegetables as well as poultry, fish, and lean meats. Whole fruits are fine, and better than juices because they have more fiber you need. Don't fry food. Use healthier methods and healthy oils.
If you are 5'10 I would not try to get to 100lbs. That is very underweight for your height. 13 is when all children boys and girls start to gain but lose it within a year as if it never happened. I wouldn't be too worried about your weight at all.
Why do you want to be underweight? If you love sports you most likely have a lot of muscle mas making up your current underweight BMI. Get a fat percentage measurement done and you may find that you should actually worry more about properly nourishing and taking care of your body's needs than losing weight. Don't hurt yourself, and your body will continue to play sports. Underweight is not good.
Sorry, you are not underweight now, but a few less pounds and you will be. Work on your muscle strengthening. More muscle less fat.
as a ballet dancer, i was 5' 9" and 125lbs at the age of 13. I am 23 years old now (and still dancing). that is the lowest my weight ever was, and will never be that way again.
Why? because my stamina fell and I could not keep up with everyone else in my ballet company. after a certain point of weight loss, you will begin to lose muscle, not fat. this is a very dangerous thing for a girl your age, or anyone of any age for that matter. At one point I was you, and I thought I was too big at 130lbs. but honestly when i look back at the images of myself from that time period, i ask myself "why did i think i was too big? i looked great." if i had focused more on my health and less on my weight, i would have been happier, healthier, less injured, and a stronger dancer and athlete. You are an excellent weight that is very low for your height, and if you are active you should work on maintaining a strong healthy body, not necessarily a small body.
if you are worried about your image, focus on the image, not the numbers on the scale. muscle really does weigh more than fat. at my smallest measurements i weighed 140lbs (and i was smaller than i was at 130lbs!). alternate doing cardio and strength training with plenty of stretching (while warmed up, never before you work out) to create long and strong lean muscles. make sure to eat at least 2-3 servings of lean protein a day, as many fresh fruits and vegetables as you want, and make sure that you are getting more than you think you need of calcium. highly active women and girls are prone to calcium deficiencies that can cause fractures are breaks in bones without much more than hoping on one foot wrong.
again at your age you should worry about proper diet, strength, and stamina more than the numbers on the scale. it sounds like you have a wonderful body, and just need to find some confidence in yourself. good luck.
Its hard to say this without sounding patronising or saying things that may be taken the wrong way, but honestly, though BMI is not that accurate, It sounds like you are focussing on your weigh too much as 100lbs would make you underweight, You are at an age where your body shape is going to change and as a woman this will mean if you are not malnourished things like the proportion of your body parts such as your hips and butt will change from what you are used to. Its also normal to put on a little weight at this stage, If you want to look good then embrace this and keep up the sports, Focus on fitness not weight. if you do will find that weight to be the right shape and in the right places. If you try to hold on to your childhood figure you may end up looking very unhealthy despite being thin.