The Constitution was completed on September 18, 1787. After its completion, it was sent to be ratified by the states. If nine states ratified the Constitution, it would be considered valid and put into effect.
81 days after the Constitution was completed (on the 7th of December), the state of Delaware ratified it. Delaware was the first state to ratify the Constitution, followed five days later by Pennsylvania.
After Pennsylvania, New Jersey, Georgia, Connecticut, Maryland, South Carolina, New Hampshire, Virginia, New York, and North Carolina ratify the Constitution. On March 24, 1788, Rhode Island had rejected the constitution, but almost two years later, (May 29, 1790), they agreed too.
The Antifederalists didn't want to ratify the Constitution because that would mean more taxation, from the states and from the federal government. The Federalists thought that taxation was necessary for the federal government because it supplied the money it needed for the military force of the union and for paying debts incurred by the American Revolution.
Rhode Island and North Carolina didn't want to ratify the Constitution because it didn't have a Bill of Rights for the citizens. When that was added, they ratified too. The Bill of Rights comprises the first ten amendments to the Constitution of the United States. It was written by James Madison in 1791 and gave Americans rights like freedom of speech, of religion, and of press.