Vitamins in Infancy

Babies may need extra vitamin C and vitamin D 

There are only small amounts of these in milk  as it comes from the cow or  in solid food that are given early. Breast milk may contain sufficient vitamin C if the mother's diet is rich in citrus fruits and certain vegetables. Babies on an evaporated milk formula should receive 25-50 milligrams  per day of vitamin C in a commercial preparation until  they are received 2 ounces of orange juice daily. It does no harm for  breast-fed babies to take this too, as an extra precaution.
In the United States, pasteurized milk or ready-to-use formulas contain 400 units of vitamin D to the quart, and a can of concentrated prepared formula or evaporated milk contains the same amount. This should be sufficient to prevents rickets in a normal baby. But breast milk may not contain enough vitamin D, so a breast-fed baby should receive 400 units daily in a commercial preparation. 
Most bottle-fed babies in the United States are given commercially prepared formulas which are vitamin-fortified so they don't need any added vitamins in infancy. Your doctor can tell you whether or not your baby needs extra vitamins.
If you are breast-feeding, your doctor will advise you about giving a 3-vitamin preparation that contains C, D and A. 

Attention! Excessive doses of vitamin D can be harmful.

Drinking Water for a baby

If there's no fluoride in your drinking water, your doctor will prescribe it, either in the baby's vitamin drops or separately. 

Some babies want water, some don't

It is sometimes recommended that a baby be offered a few ounces of water between meals, once or twice a day. It isn't really necessary, because the amount of fluid in breast milk or formula will satisfy the baby's ordinary needs. It is more important to offer water if the baby has fever, or during excessively hot weather, especially if his urine turns dark yellow and he appears extra thirsty.  

As a matter of fact, a lot of babies don't want any water from the time they are a week or two old until they are about a year. During this age they fairly worship anything with nourishment in it, but they feel  insulted by plain water. If your baby likes it, you can give it to him once or several times a day between meals.

Text source: Dr. Spock's Baby and Child Care -Beanjamin Spock and Michael Rothenberg