Since there is no official definition of class, determining what class a person belongs to is generally an inexact process. In the United States, the very most important determinant of a person's social class is their income and wealth.
In the United States, class is almost solely a matter of wealth and income. There are some people who make a distinction between "old money" and "new money," but these people are few and far between. Education does play a role, but a person with a graduate degree and a middle income has little in common with a person who has a graduate degree and a high income. Class in the United States is very much determined by the size of house you can afford and the amount of money you can spend on vacation or on sending your children to private school. It is not based on religious affiliation or birth or race or any of these other things that might be markers for class in other countries.