Below is a summary of the sailing rules that apply most often on the race course.  This summary is intended as an aid to sailors and not as a substitute for the Racing Rules of Sailing, a copy of which all racing sailors should own. 

RIGHT-OF-WAY RULES

PORT-STARBOARD.  Port-tack boats must keep clear of starboard-tack boats.  (Rule 10)  Note:  You are "keeping clear" of another boat when she doesn't have to avoid you.

WINDWARD-LEEWARD.  When boats are overlapped on the same tack, the windward boat must keep clear.  (Rule 11)

ON SAME TACK, ASTERN-AHEAD.  When boats are on the same tack and not overlapped, the boat clear astern must keep clear.  (Rule 12)  Note:  One boat is "clear astern" if she's entirely behind a line through the other boat's aft-most point, perpendicular to the other boat.  The other boat is "clear ahead."  Two boats are "overlapped" if neither is clear ahead of the other.

TACKING TOO CLOSE.  Before you tack, make sure your tack will keep you clear of all other boats.  (Rule 13)

LIMITATIONS ON RIGHT OF WAY

If the other boat must keep clear, you have "right of way". Even if you have right of way, there are limitations on what you can do:

AVOID CONTACT.  You must avoid contact with other boats, but a right-of-way boat will not be penalized under this rule unless the contact causes damage.  (Rule 14)

ACQUIRING RIGHT OF WAY.  When you do something to become the right-of-way boat, you must give the other boat a chance to get away from you.  (Rule 15)

CHANGING COURSE.  When you change course, you must give the other boat a chance to keep clear.  (Rule 16)

ON THE SAME TACK; PROPER COURSE.  If you are overlapped to leeward of a boat on the same tack, and if just before the overlap began you were clear astern of her, you cannot sail above your proper course (i.e., the course that will take you to the next mark the fastest) while you remain overlapped.  (Rule 17.1)

PASSING MARKS AND OBSTRUCTIONS

There is a set of special rules for boats that are about to pass a mark or obstruction.  However, these special rules don't apply between boats on opposite tacks on a beat to windward.  (Rule 18.1)

Except at a starting mark, you must give boats overlapped inside you room to pass a mark orr obstruction, and boats clear astern must keep clear of you.

There's a two-length zone around marks and obstructions, and a boat's rights and obligations with respect to another boat are "frozen" when the first of them enters that zone.  If you are clear astern of another boat when she enters the zone, you must keep clear of her until both boats are past the mark or obstruction, even if you later become overlapped inside her. (Rule 18.2)

TACKING NEAR A MARK.  Don't tack within the two-length zone at a windward mark if you willl cause a boat that is fetching the mark to sail above close-hauled to avoid you, or if you willl prevent her from passing the mark. (Rule 18.3)

ROOM TO TACK AT AN OBSTRUCTION.  When boats are on the same tack on a beat and come to an obstruction, the leeward boat gets to decide which way they are going to pass it.  If the leeward boat hails for room to tack, the other boat must give it to her; but the leeward boat must give  the other boat time to respond before she tacks. (Rule 19)

OTHER RULES

Before your Preparatory Signal, and after you finish, don't interfere with boats that are about to start or are racing. (Rule 22.1)

If you break a rule while racing, get away from other boats and do two 360-degree turns; if you hit a mark, do one turn. (Rules 20 and 44)  Note:  Sometimes the Sailing Instructions require you to fly a flag acknowledging that you broke a rule, instead of doing turns. 
(Rule 44)

If you start too soon, keep clear of others until you get behind the line again.
(Rules 20 and 29)