What does the Supreme Court do to a law once it is passed?

Nothing, unless a party with standing to challenge the law files suit against the United States in US District Court, the losing party appeals the case to the appropriate US Court of Appeals Circuit Court (usually), and the subsequent losing party files a petition for a writ of certiorari (request to review the case) with the US Supreme Court.

If they grant cert (accept the case), the Supreme Court will evaluate whether the law conforms to the US Constitution either in general, or as applied. If the Court determines the law is unconstitutional, it will be nullified and rendered unenforceable.

It is important to note that the US Supreme Court does not systematically review every law Congress passes. Someone who is severely and directly, negatively affected by the law, and has a grievance that can be resolved by a court, must file suit and exhaust the required appeals process before the Supreme Court can review the case (and the law).