Hi, and welcome to the forum.

Public (i.e. state) schooling in the US is free. Generally, children go to the school that serves the district in which they live - which is why homes in good school districts command higher prices than those in lesser school districts.

Generally kids must start school at age 6 (Grade 1) and since you son will be 6 in September, he'll probably be eligible for 1st grade this year. The cut-off date for turning 6 is usually October 1st or so, though it's often possible to appeal if you feel your child is socially behind or ahead of his cohort group.

If the district has Kindergarten (and many, if not most, do), the starting age is generally 5. Younger than that, there are a variety of nursery school, day care and other options - usually paying.

Private schools are also available, in a wide range of varieties, options and (of course) prices.

Oddly enough, the Wikipedia article on the Los Angeles school district Los Angeles Unified School District - Wikipedia, the free encyclopedia gives a reasonable overview - though in many big cities the public schools are not terribly well regarded. There is also quite a bit of information available simply by googling "schools in Santa Monica" and "private schools in Santa Monica."

When you start looking for accommodation, you'll find that the (real) estate agencies in the area are often good sources of information about schools in the area (because it affects the cost of housing). There are some real estate websites that can direct you to fairly extensive ratings and reviews of area schools.
Cheers,
Bev