There's quite a few different races series going on at any time. All you need to do is find one that you like the sound of and post in the thread concerned saying you'd like to take part. There'll be some rules for each race that you will need to follow which generally consist of which Track, Arcade or Free Run, Date/Time of submission, Arcade or Garage cars, number of laps, list of modifications allowed etc...
It's really quite simple, but if you have any other questions there are plenty of people around to help!
Well, make your own, dude! I imagine you're not the only one on here who's like "well dang, I'd like to join that Laguna Seca series (for example) but..."