The NICU will use a scoring system while they determine how much withdrawal the baby is going through. It really depends on how much the mom was taking and the babies response, not all withdraw in the same way to the same amount.
Examples of symptoms are low grade fever, high tone, disorganized sucking and swallowing, sneezing, yawning, frantic sucking, difficulty with state transition (awake to asleep, etc) sleeping for short periods say only an hour after feeding and being awake way too much for a newborn, tremors, diarrhea, overeating, mottled skin, breathing fast, snuffy nose, diaper rash.
An occupational therapist who works with infants can also be helpful in giving you tips on how to calm and sooth an infant in withdrawal. For instance, deep pressure after swaddling and implementing the 5 s''s but you may have to be more persisitant. They generally need holding or calming much of the day, we use volunteers if we have them.
Treatment is to give the baby morphine or methadone if needed when symptoms are severe, and then gradually reduce the amount every few days as the condition allows. The worst withdrawal symptom is seizures, so generally the treatment is to prevent seizures that can harm. The process usually takes up to around 6 weeks, although I have seen one need 8 for a mother who had rheumatoid arthritis from childhood and was on major pain meds and methadone to prevent withdrawal.