Depending on whether you are nursing your baby or formula feeding your baby, a 2 month old baby should eat approximately every 2 to 4 hours. Formula fed babies generally go longer between feedings due to the harder to digest nature of formula vs. breast milk.
Babies at this age will typically let you know when they are hungry. They will generally indicate hunger by sucking on their fingers, crying, or being agitated. Feeding schedules can vary widely depending on if the infant is formula fed or breastfed, but generally speaking infants this age will feed every 2-3 hours.
Every two to three hours if breastfed and three to four if formula fed. If the baby is over 13 lbs. , then the baby can go longer and even possibly if you are very lucky, all night long. This is most often not the case and the baby will still wake at night to eat.