Just after the ratification of the Declaration of Independence the Continental Congress assigned a group to draft a government for the new state. The document they came up with, the Articles of Confederation, was the controlling law of the United States from its adoption in 1777 until the Constitution took effect in 1889 1789.
This document was designed, as its title suggests, to make the United States a weak confederation of sovereign states, retaining all powers to individual states except those explicitly reserved to the central government. The Congress had responsibility for external affairs, including the military, but had no power over trade and little power to levy taxes (it usually had to resort to asking the states to send money to help pay for things, like the Army). Additionally, it required unanimous consent from all 13 states to carry out most tasks.
So how was it led? With significant local autonomy. In an era before mass communication and transportation this would have had to happen anyway, but the central government couldn't even get the treaty to end the Revolutionary War signed because several delegates to the Congress didn't bother showing up.
How did it survive? Through luck, foreign aid, and the military skill of George Washington and several key subordinates. Once the war was over Washington and his allies began agitating for a stronger central government based on their experiences during the war.
The one bright spot of the Articles of Confederation was in land policy - the Land Ordinance and Northwest Ordinance both set the standards for admitting new states to the union, as well as the ways of surveying and apportioning new land, that formed the basis for this process throughout the nineteenth century.
Finally, I have a question for you: Is the Articles of Confederation no longer on the curriculum for American schools? This isn't a knock on you - you were taught what you were taught. But I remember learning this as early as elementary school in a basic way, and quite extensively in high school. It would be a shame if they don't cover it any more. The period of weak central rule from 1776 to 1789 is one of the key influences on American federalism and the Constitution's emphasis on federal over local power.