How can a 13 y.o. girl improve her fitness?

First!: Have you entered puberty? If you have, then start doing physical activities that you enjoy. Try a cardio activity and combine this with resistance exercise, weights, dumbells, or machines. It is easier to exercise if you do it with someone. On starting your cardio, get a simple heart rate monitor and try to start at a level that takes you to 140 bpm. That is close (slightly less) minimum level.