What is a normal sleeping schedule for a young baby?

Irregular. Most newborns and small infants have fairly irregular sleep schedules. The universal truth is that they do sleep a large portion of the day with most newborns sleeping up to 18 of 24 hours. The patterns of sleep, however, can be very irregular in the first eight weeks of life. Many parents experience the challenges of this, but don't despair. Regular sleep patterns do eventually develop.
Sleep 16-20 hrs/day. Young babies need to eat every 3 hrs so sleep fits in between these feedings. However after about 3 months many babies may start getting into a routine of naps (varying lengths of 20min to 3 hrs) a couple times a day and can go longer (up to 8 hours!) during the night. As they continue to get older babies will sleep longer at night and go from 3 to 2 naps during the day.
This varies with age. The newborn often sleeps 18 hrs/day & may vary with growth spirts. The schedule can be shaped by the way you set up a pattern. Babies, like adults, have one deep sleep period/ day that you should set for your deep sleep time. Even newborns can go 4-5 hours, waking you to start their day pattern. Allow 4 parts: two hrs of rest/wake to feed/ maintaince/ play until tired/ repeat. No day nap > 3 hr.