Hi Sarah, 

Welcome to the sport of triathlon. While the number of rules can seem overwhelming, don't despair! Familiarize yourself with the rules often, attend pre-race meetings and take the opportunity to ask race directors and race officials for clarification of rules that are unclear. Keep in mind, too, that professional triathletes have a different set of rules and some of them are directly opposite of age group rules.       

Below are some key rules copied directly from 
USA Triathlon's flyer "Remember the Rules."  
You can also visit, www.usatriathlon.org for the most up to date and current rules.

To avoid Position Violations:
1) Ride on the right side of your lane.
2) Pass on the left of the cyclist in front of you, never on the right.
3) Keep three bike lengths between you and the cyclist in front of you.
4) If you enter the draft zone of another cyclist, complete your pass within 15 seconds.
5) If passed, drop out of the drafting zone, to the rear, before attempting to re-pass.
Other rules to remember:
1) Race numbers: Keep them visible and wear at all times.
2) Equipment abandonment: No garbage, clothing water bottles, swim gear etc shall be thrown on the course. 
3) Headphones: Are not to be worn at any time during the race.
4) Helmets and chinstraps: Must be worn and fastened properly at all times while on the bike.
5) Un-sportsmanlike conduct: Treat other athletes, volunteers and officials with courtesy.
6) Race bandits: You must receive the race director's permission to transfer your race number to someone else.

Always go to pre-race meetings, review the rules materials included in your packe and then stick to those rules to ensure safe and fair racing.

Good luck!
Rachel