Answering the question "What does the Constitution say about slavery?" is a little tricky because the words "slave" or "slavery" were not used in the original Constitution, and the word "slavery" is very hard to find even in the current Constitution. However, the issues of slaves' rights, the slave trade, and slavery have been addressed in several places of the Constitution; namely, Article I, Articles IV and V and the 13th Amendment, which was added to the Constitution nearly 80 years after the signing of the original document.
The Three-Fifths Compromise
Article I, Section 2 of the original Constitution is commonly known as the three-fifths compromise. It stated that slaves counted as three-fifths of a person in terms of representation in Congress, which is based on population. The compromise was struck between those who argued that slaves should not be counted at all and those who argued that all slaves should be counted, thereby increasing representation for slave states. Slaves did not have the right to vote, so this issue had nothing to do with voting rights; it merely enabled slave states to count slaves among their population totals. The three-fifths law was, in effect, eliminated by the 14th Amendment, which granted all citizens equal protection under the law.
Prohibition on Banning Slavery
Article I, Section 9, Clause 1 of the original Constitution prohibited Congress from passing laws that banned slavery until the year 1808, 21 years after the signing of the original Constitution. This was another compromise between Constitutional Congress delegates who supported and opposed the slave trade. Article V of the Constitution also ensured that there could be no Amendments that would repeal or nullify Article I before 1808. In 1807, Thomas Jefferson signed a bill abolishing the slave trade, made effective January 1, 1808.
No Protection in Free States
Article IV, Section 2 of the Constitution prohibited free states from protecting slaves under state law. In other words, if a slave escaped to a free state, that state was not allowed to "discharge" the slave from their owner or to otherwise protect the slave by law. In this case, the indirect wording used to identify slaves was "Person held to Service or Labour."
The 13th Amendment refers directly to slavery in Section 1:
Neither slavery nor involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted, shall exist within the United States, or any place subject to their jurisdiction.
Section 2 grants Congress the power to enforce the Amendment by legislation. Amendment 13 formally abolished slavery in the US, but it didn't come without a fight. It was passed by the Senate on April 8, 1864, but when it was voted on by the House of Representatives, it failed to receive the required two-thirds vote for passage. In December of that year, President Lincoln appealed to Congress to reconsider the Amendment. The House did so and voted to pass the Amendment by a vote of 119 to 56.