One of the best ways to learn what goes on in Motorsports is to visit the track. While going to high profile events like NASCAR, Indy or Formula is a great way to experience an event you might get more out of visit the local track on a club racing weekend.
You can learn a lot about the local clubs SCCA, NASA, PCA, BMWCCA by checking out their website for when the next event is on and going to the track. Most of the time you can get in free just signing a liability waiver at the entry gate. Park your car in an out of the way spot and you can explore the paddock.
No better way to learn more about the type of racing then by talking to the racers that do it. Don't be afraid to start a conversation or ask questions, all racers got started somehow. Almost all racers are friendly, welcoming and happy to talk about their race car. Of course if they have the car half torn apart with tools all over the place trying to get it fixed for the next session you might want to talk to the next person and come back later. Take you time and explore, you will probably see a wide variety of cars and different activities going on, you can even take photos, go sit in the stands and watch a race or two.