How can obiter dictum become part of a ratio in a case?

Do you mean rationale? If so, obiter dictum is, by definition, not part of the rationale for deciding a case. It is extra language inserted by the judge that is not necessary in deciding the case.

For example, in Dred Scott v. Sandford, Chief Justice Taney writes in the opinion that African-Americans are not and cannot be citizens, thus Dred Scott didn't have the right to sue in federal courts. Chief Justice Taney should have stopped after that, because if Dred Scott didn't have a right to sue in federal courts, then the Supreme Court has no jurisdiction and the case should be dismissed. However, Taney goes on to say that slavery can't be banned in any state or territory because it's a violation of the due process clause. This is all obiter dictum, it has no relevance on the decision of the issue presented before the Court.