The decisions of the United States Supreme Court are final and binding on the parties to the case on which the decision is rendered. Furthermore, as to the specific, narrow, issue on which the case turns, it is binding on everyone subject to U.S. legal jurisdiction.
For example, if the USSC had ruled that the mandate of the ACA was an unconstitutional exercise of power by Congress, then the IRS would be prohibited from assessing the penalty associated with not having health insurance. The IRS and Congress are bound by the decision.
The decision can be "overturned" in a couple of ways. Congress could modify the law to make it Constitutional, pass a new law that meets the Constitutional requirements (as defined in the USSC decision), or a later USSC - perhaps with a couple of new members - could rule IN ANOTHER SIMILAR CASE that the mandate is Constitutional.
As a private citizen, there is nothing you can do to affect the relevant Constitutional law as defined by the USSC, even if it is patently incorrect, as it was with many death penalty cases in the '60's. All you can do is vote for a President and Congresspeople who take the Constitution seriously (or for Progressives, who try to ignore the Constitution altogether), and hope that over time the USSC will be controlled by people who share your views.
Alternatively, if you are motivated and unscrupulous enough to consider assassinating rogue USSC justices...