During the period between the Revolution and the Constitution, the states were joined in the Articles of Confederation. The Articles didn't include a position called "President" (and in fact opposed the notion of a strong executive).
The Articles were ineffective - the government was unable to collect taxes or implement policy and there was widespread discontent at the "licentious behavior" permitted by the Articles. Several leaders summoned the Annapolis Convention to try to find a way out of the problem. The participants decided that the problem could not be solved; they called for a broader convention in Philadelphia that became the first Constitutional Convention.
George Washington was one of the movers and shakers of this period. Although retired from public life he carried out extensive letter writing campaigns and hosted strategy sessions at Mt. Vernon.
In addition to the wikipedia pages, I'd recommend Pauline Maier's Ratification.
I'm going to repeat called2voyages excellent recommendation, because comments are ephemeral.