The evidence that Chief Justice Taney draws from in making this claim comes from the Declaration of Independence and the Constitution and from what we can clearly infer about the beliefs of the people who wrote those documents.
Taney starts with the assertion that African Americans were not considered to be citizens by the people who wrote the Constitution. He does not provide any evidence from this assertion at that point. Later, he says that there are two clauses of the Constitution that refer to African Americans. In both cases, the clauses imply that it is proper to think of African Americans as property.
Taney also points out that African Americans were not considered to be equal by the people who signed the Declaration of Independence. They were willing to subscribe to the idea that all men were created equal. They were, at the same time, willing to allow slavery to exist and even to keep slaves themselves. This clearly shows that they did not consider African Americans to be on the same level as whites.
For these reasons, Taney says, it is clear that African Americans are not to be seen as citizens.