How much does my two month need to eat?

Depends. Usually 24-32 oz a day or 6-8 nursing sessions.
Newborn feedings. A two month old usually eats/drinks 3 ounces of formula every 3 hours at least; this equals 24 ounces of formula a day; many babies will drink more, sometimes 32 ounces a day; be sure to take the baby for regular check ups with his doctor, beginning at two months then every two to three months the first year; the doctor will have pamphlets to hand out about baby's feeding and development.