What method did the Federalists employ to get their views across to the people? What were their arguments, and how did the "Antifederalists" respond?

The main method they used was publishing a series of papers pushing for the ratification of the Constitution called the "Federalist Papers". They argued that a strong central government was needed to pay back war debts and control the economy. The Anti-Federalists insisted that there would at least need to be a Bill of Rights in the Constitution.