Each child is an individual and so this varies widely. My niece sleeps about 10 hours whilst my nephew is good on about 8 hours. And napping stopped for them both when they hit the age 4 mark, maybe the odd case of falling asleep if in the car to long. However, on average:
A child aged 12 months needs around 2½ hours during the day and 11½ hours at night time.
A child aged 2 years needs around 1¼ hours during the day and 11¾ hours at night time.
A child aged 3 years needs about 1 hour during the day and 11 hours at night time.
A child aged 4 years needs no sleep during the day but 11½ hours at night time.