Just about every hockey stick has a curve built into it's blade. Looking down the shaft of a stick, the blade either curves to the right or the left. If it curves to the right, it's a Left Handed stick. If it curves to the left, it's a Right Handed stick. Clear as mud right?
Typically, a hockey stick is held with two hands like a shovel. The hockey stick gets its right or left hand designation from which hand is closest to the blade of the stick. The hand on the top end of the stick should be your stronger, or dominant hand. So, if you are right handed, then your dominant hand will be your right hand, thus it will be at the top of the stick, therefore you should be using a Left handed stick.
Watch a hockey player and you'll see that 90% of his/her time with a puck is spent stickhandling or passing. The other 10% is spent shooting, typically a wrist shot, or a slap shot. It’s because of this that it is essential the hand at the top of the stick, the one with the most control of the stick should be the dominant hand.
When a player is on a breakaway, typically he will use one hand to hold the stick and push the puck forward. It makes sense that the dominant hand is at the top end of the stick. That hand never lets go of the stick. The lower hand is there to provide support and additional power (and to push the opponent away). Watch a right-handed player who uses a right handed stick on a breakaway, and few of them will be able to control their stick with their left hand. Their speed and agility suffer.
So, to sum this all up, typically speaking if you are a right handed person, you should be using a left handed hockey stick. If you are a left handed person, then you should be using a right handed hockey stick.