With none or very short maternity leaves there is a wide need for nursery care for even very young infants. As there are no public systems covering this part of child care there are many more private nannies and au pairs than in many European countries.
As the new initiative to bring pre-school to everybody hasn't been quite implemented yet, the lack of a public system leaves room for many private nurseries and day care centers. If not cared for at home, children are typically in a nursery until they are out of diapers. Day care covers normally 3-5 year olds. As older children advance into the school system by summer vacation this is also the time that day care institutions get openings. But they already sign up for these openings in January-March, so if you plan on moving with children and know which area you plan to live in this is another item for the to-do list before you have even packed your suitcases. Otherwise be prepared for looking after your children yourself.
Many private child care institutions are very hard to get into with entry tests and they cost a fortune. It may cost as much to have your child in one of the prestige preschools in San Francisco for a couple of years as you would expend on taking a Masters Degree on Stanford. Even quite normal preschools easily cost over $1500 per month. If you belong to a church there may be a preschool in connection to the church where children of the congregation may spend their days for a smaller fee.
Once your child reaches school age remember that the school doesn't know that you have an incoming student unless you tell them. Again, check when the school opens for enrollment and note that many schools have a "first come, first serve" policy. It is not guarantied that your child will get into the local school even though you live in the primary area. And even if you child has been accepted, unless you show up on the first day of school, the place may be given to somebody on the waiting list. Many families, who have spent the summer in their country of origin, come back to find that the child suddenly is not going to school around the corner after all.
As with the private preschools private schools may have entry tests. For some of the parochial schools one of the tests may be if the parents have attended the church and paid handsomely to the collection plate. (Use named checks so you can prove your good will.)