The party that wants the precedent reversed loses in the lower court (because the lower court is bound by current Supreme Court precedent) and appeals to the Supreme Court. The canonical historical example is Brown v. Board of Education, which was appealed to the Supreme Court explicitly to ask them to reverse Plessy v. Ferguson, which lower courts had relied on as precedent.

Somebody has to bring a new case that presents a novel legal theory/presentation that isn't clearly addressed by the ruling that forms the precedent.