A little more specificity in your questions might help. The rules of tennis are pretty simple, and you could get a lot just through watching some major tournament play on TV. As for high school and college competitions in the U.S., they take place under pretty much the same organizational structure as do other sports. Teams compete in "conferences", and there are tournaments. The NCAA governs the national collegiate level competition, and there is an annual national championship tournament.
Fewer schools have tennis teams than, say, basketball or football teams, however. My high school never had one, for instance.
caw