Determining your dominant hand when first playing golf is important in helping to develop as a player. Neither hand has an advantage in the game--both lefties and righties are successful. You will find much more success hitting the ball for distance and accuracy from your dominant side. Knowing your dominant hand is also essential when picking out the proper clubs.
A good start to figuring out which hand is dominant when swinging a golf club is to evaluate other parts of your life. Determine which hand you hold your fork with and which had your write with. Often times, this dominant hand will be the same as the dominant hand used for playing golf. This is not always a perfect measure, though. Think about which side of the plate you swing a baseball bat from. You will probably most comfortable swinging a golf club from the same side of the ball. As a right-handed hitter, or golfer, you will stand to the left of the plate or ball with your left hand at the bottom of the bat or club. The opposite is true if you are a lefty.
The best way to determine which hand is dominant when playing golf is to go out and practice swinging a club. Go to a driving range with a right and left handed club and practice hitting the ball. As a beginner, swinging the club might be awkward from both sides, but one side should feel smoother and more natural than the other. Get into a proper golf stance with your feet a little more than shoulder width apart and the ball just slightly closer to your front foot. Take your backswing, the swing forward, connect with the ball and follow through. After a few tries, it should be clear which side is dominant.
Buy a Set
Buy or rent appropriate golf clubs. Clubs are made specifically for right-handed or left-handed players and will be backward if you purchase the wrong set. As a beginner, it is best to find a place that will rent clubs to you. Most golf courses have rental sets. You can buy cheap used sets from stores like Play It Again Sports or by ordering online at a site like ebay.com.