The scoring system is fairly simple. In sparring, you try to score 3 legitimate points on your opponent, defined as a solid kick or straight punch (no hooks, backfists, uppercuts, etc) to the body anywhere between the shoulders and the waist, front, back, or sides, or a solid kick to the side or back of the head, not to the face, and no punching to the face. Solid contact is defined as controlled power, not FULL power. Ho holding, throwing, or joint locks. Junior events (up to 16 or so) generally consist of a single 3 minute round, or two three minute rounds with a 1 minute rest between rounds.
Basically, take everything that you've ever seen in the movies like "Karate Kid." "Best Of The Best," "Sidekicks," and all of the others of their sort and toss it out the window. Everyone wears full protective equipment and follow strict rules as to contact and legality of strikes, or they forfeit the match.
Forms are a group of movements used to illustrate expertise in the particular techniques required for the individual's belt rank. Think of a presentation of a mime performing a slow interpretation of a fight with an individual opponent. Forms are judged by quality of technique and memory of the specific movements of the specific form.
That's a simplified version, of course, and the governing board of each individual style tends to put their own particular interpretation of those general rules into their tournaments.
Hope that helped without confusing you too much.