Usually by age 2 to 3, you'll be able to tell whether your kid's a righty or a lefty, although your child may start showing signs of favoring one hand over the other much earlier or later. A baby as young as 6 months may be more likely to grab toys with a certain hand, for example; some children may use both hands equally until they start school and learn to write, after age 5 -- and that's totally normal too. But before a year, your baby should mostly be experimenting with both hands. If you see your baby always using one hand over the other, let your pediatrician know. This might be a sign of poor muscle or motor development in the underutilized hand.
Hand preference is mainly based on your child's unique nervous system and genetics. If at least one grandparent on each side of your child's family is left-handed, the chances are higher that he will be too. If you or your partner is left-handed, the odds are higher (and even more so if you're both lefties). There's really no way for you to influence your baby's handedness, and you shouldn't try to change it.