Bodyfat is a catch-22 - In that it is a ratio of lean muscle mass to bodyfat. To illustrate the extremes - an ultra skinny marathon runner can actually come out w/ a higher bodyfat% than you'd expect - not because he is fat, but rather because he has a very low lean muscle proportion. The other extreme is a heavy person who does actually have a high % of bodyfat and lower muscle mass. It is a ratio of the two - so it matters more what is your body composition.
For you, although you're 16, for your height, I'd venture that you have a light frame (i.e. "small boned") and don't carry much fat, but maybe lower muscle mass too (most girls do). (I'm comparing to myself - I'm 5'7" and when I was 16 I was probably more like 130-135 lb. I am probably medium build, but tend to put on both fat & muscle easily.)
There are a couple ways to measure bodyfat. The most accurate is hydrostatic / Bod Pod approach but this can cost some cash and you need access to a facility to do it. The easier way (less accurate, but reasonable to get a ballpark) is using skinfold caliper testing. Here are a few places that describe how to do it and then do the calculation:
Body Fat Calculator 6 formulas to calculate body fat percentage
The "easiest" way is to just get one of those scales that measures bodyfat via bioimpedence - e.g. a Tanita scale. These measure "accurately" in the sense of to a couple decimal places, but the method of measurement is highly dependent up on the amount of water in your body at the time of measur e- mostly the point is that if you want to measure day-to-day changes, it can be hard because you don't usually have the same amount of water in your system every time you measure. Im' not just talkign about how much water you drank, but rather if your body is holding water e.g. that time of the month, you ate a lot fo carbs the night before, etc. Just inconsistent measuring environment.
THe above is just some info to give you some places to start if you have questions about bodyfat. To set a benchmark - most women are in the 20-25% range of bodyfat - this is what is considered "healthy". If you start comparing to athletes, you are probably looking at closer to 12-14%. Men will be leaner because they don't have the estrogen component (the stuff that makes us women & makes our bodies optimized for child-bearing).
My best recommendation to give you a good all-around intro to training & nutrition is Bill Philips' Body for Life book. Its been around for many years now and you can probably find it at your local library or in the book store for $10-15. It is a reasonably quick read but covers all the important details of "how it works" and "why it works" in a readable way. The program recommends a diet framework but does not constrain you to a rigid meal plan. It also outlines a good training schedule that doesnt' require several hours/day in the gym. IMO it is a great place to start. (Note - you don't need to buy the EAS products that Bill lists in the diet - but rather you can look at those products and find comparable ones (e.g. in total amount of protein, fats & carbs in each) to substitute. The idea is also not to imply protein bars and shakes should be a staple in your diet - but rather they are a convenient way to get in some extra protein, etc. YOu can also substitute real food for those meals.
Hope that helps. Here's a link to the Body for Life book so you can see which I'm talking about. There are some variations of it (e.g. women-specific, etc.) I think they are all comparable, so whatever one you can find for the cheapest is what I would do. The real goal I have in recommending this is not that you follow THAT diet, but rather that it is a great foundation book to start with. The most successful "diet" is the one that you make part of your lifestyle - not a 12 week strict program you do and then go back to how you used to eat. Its about establishing good habits and understanding more about nutrition.
Amazon.com: Body for Life: 12 Weeks to Mental and Physical Strength (Audible Audio Edition): Bill Phillips, Michael D'Orso: Books
I'm sure as you read you will come up w/ more questions. Please feel free to ask! It can be confusing - its not rocket science, but its not intuitively obvious. It is also skewed by the media selling specific "diets" - you don't need a "diet". You need good basic eating & exercising habits.