Like surfers, some snowboarders ride"regular," with their left foot forward, and some ride "goofy-footed," with their right foot forward. Which is right for you doesn't necessarily correspond to whether you're right- or left-handed.
Snowboarders have devised all sorts of formulas and indicators to determine which foot to put forward and which to the rear. For instance, it's been suggested that your forward foot is whichever one you plant beside a ball when you are about to kick it. But all these tests boil down to one thing: personal preference. Try strapping on the board both ways, and go with whichever arrangement feels best.
Which foot you put forward will determine whether you face toward the left or right edge of the board. This also establishes which is the board's "toe edge" and which is its "heel edge." For a beginner, it's generally easier to make a toe-edge turn because you can control the board's tilt with the calf muscles.