Our experiences have been with the California school system so you can see more under the California location.
As a general rule, if English is not your native language and you have school age children, it pays to look over the shoulder and take serious interest in their education. Not only because they will take their clues about the importance of education from your behavior, but also so you can learn what they learn. It is very useful to know the English proverbs, the local history and geography, and you may even benefit from knowing the English words for grammatical and mathematical terms. You will not be a good help for your kids if you can't help explain their homework in words they can relate directly back to the class room. They say fractions, you say - well, whatever you say in your native language, but if it isn't one of the latin-based languages fractions are probably called something totally different.
You can check the academic standing of the public schools on www.greatschools.org as well as read comments for both public and private schools.
The public school system goes from Kindergarden to 12th grade, typically divided into Elementary School (K-5), Middle School (6-8), and High School (9-12).
There are private schools, many are in connection with a church, where you can shell out $15-50,000 per year. Public support for private schools are - at least in California - only through a tax deduction of your costs. Private schools typically require entrance examines. If you want to get your child into one of the parochial schools, it will benefit your standing if you attend the church in advance and pay handsomely with personal checks into the collections basket.
In areas where there are many immigrants from the same country you may find national schools. These can either be accredited so attending them replace going into American schools, or there may be typically Saturday school where focus is on the language of the home country. Some countries have emigrant-associations that provide online education for their citizens abroad, check the web for what applies in your country.
In some high schools you can take the International Baccalaureate.
Finally there is Home schooling. Almost 2 million American children are home schooled, and only around 1 in 3 of these children are kept home for religious reasons. Some live in very rural areas, some just don't fit into the public system. Parents may group together so the home schooling really is a small private school where the parents share teaching a small group of children in whatever subjects they are best at and the children have a chance to socialize and make friends. Some home school for a year or two because a child is sick or - like some of our friends - because they decided to live two years on a boat sailing from Nova Scotia to the Bahamas and back.
There are special home school providers who for a fee will teach the kids through the internet, deliver appropriate materials, run tests, and guarantee that state requirements re. curriculum are met.