Though your child may have started to show a preference for his right or left hand, you won't be able to determine true right- or left-handedness until he's 2 or 3 years old, when he'll begin to favor the same hand consistently. Some children may be ambidextrous (using both hands equally) until they're 5 or 6, when they finally make a choice.
Hand dominance is greatly influenced by genetics. If both you and your partner are left-handed, your child has a 45 to 50 percent chance of being left-handed as well. (About 10 percent of people are left-handed.)
If you're curious about which side is dominant in your child, try handing him a toy or rolling him a ball. He's very likely to reach for it with his dominant hand, which will probably be stronger and more dexterous.
If your child seems to be using one hand exclusively before he's 18 months old, talk to your pediatrician, as early hand dominance may be a sign of motor development problems.
As you watch your toddler's motor skills develop, remember that it's not a good idea to attempt to influence his hand preference. While genetics alone don't entirely explain why someone ends up right- or left-handed, hardwiring of your child's nervous system is at least part of the reason. Forcing him to use his right hand when he's really a lefty is unlikely to work in the long run and will only confuse or frustrate him along the way.