Our Constitution requires an elected president to take the following oath: "I do solemnly swear (or affirm) that I will faithfully execute the Office of President of the United States, and will to the best of my Ability, preserve, protect and defend the Constitution of the United States." With the election of George Washington as our first President of the United States, just how did we go about the first inauguration?
With no telegraph, e-mail, text or Twitter, someone had to inform George Washington that he had been (unanimously) elected President. Charles Thomson, Esquire (below) was chosen for the task.
If you've seen the Trumbull painting of the signing of the Declaration of Independence, then you have seen another representation of Charles Thomson, which was replicated on the $2.00 bill. Thomson is the gentleman standing immediately to the right of a seated John Hancock.
Thomson traveled to Mount Vernon, arriving on the 14th of April of 1789 and informed General Washington of his mission in the following words:
"Sir, The President of the Senate chosen for the special purpose, having opened and counted the votes of the electors in presence of the Senate and House of Representatives, I was honored with the commands of the Senate to wait upon Your Excellency with the information of your being elected to the office of President of the United States of America. This commission was intrusted to me on account of my having been long in the confidence of the late Congress, and charged with the duties of one of the principal civil departments of Government.
I have now, sir, to inform you that the proofs you have given of your patriotism, and of your readiness to sacrifice domestic ease and private enjoyments to preserve the happiness of your country, did not permit the two Houses to harbor a doubt of your undertaking this great and important office, to which you are called, not only by the unanimous vote of electors, but by the voice of America. I have it, therefore, in command to accompany you to New York, where the Senate and House of Representatives are convened for the dispatch of public business." 
What was George Washington's response to Charles Thomson on April 14th, when informed he had been elected first President of the United States?
"Sir: I have been accustomed to pay so much respect to the opinion of my fellow-citizens that the knowledge of their having given their unanimous suffrages in my favor scarcely leaves me the alternative for an opinion. I can not, I believe, give a greater evidence of my sensibility of they honor which they have done me than by accepting the appointment. I am so much affected by this fresh proof of my country's esteem and confidence that silence can best explain my gratitude. While I realize the arduous nature of the task which is imposed upon me, and feel my own inability to perform it, I wish, however, that there may not be reason for regretting the choice, for, indeed, all I can promise is only to accomplish that which can be done by an honest zeal. Upon considering how long time some of the gentlemen of both Houses of Congress have been at New York, how anxiously desirous they must be to proceed to business, and how deeply the public mind appears to be impressed with the necessity of doing it speedily, I can not find myself at liberty to
delay my journey. I shall therefore be in readiness to set out the day after to-morrow, and shall be happy in the pleasure of your company, for you will permit me to say that it is a peculiar gratification to have received the communication from you." 
"Washington's Reception by the Ladies on the Bridge" at Trenton, New Jersey. On his way to New York for his inauguration (1789), Washington traveled through Trenton as a tribute to the people and Battle of Trenton (December 26, 1776). After a crushing defeat and loss of Fort Washington, the victory in Trenton encouraged tired and sagging American troops to push ahead in the fight for independence. Etching by Nathaniel Currier, 1845. Gift, Ms. H. M. Taylor at The James Madison Museum of Orange County Heritage.
"The first inauguration of a President of the United States took place in New York on April 30, 1789. A general holiday had been proclaimed, and amid scenes of jubilation, the inhabitants of Manhattan Island turned out in great numbers to witness the spectacle. Shortly after noon, on the balcony of Federal Hall in front of the Senate Chamber, the oath of office was administered to the Father of His Country by the chancellor of the state of New York. With John Adams, who had just previously been inaugurated Vice-President, standing on his right, and Robert R. Livingston on his left, Washington laid his hand reverently on the large open Bible placed on a table before him, and at the conclusion of the oath, responded in a tone of vibrant solemnity, 'I swear, so help me God.' The Chancellor then stepped forward, and called out to the enormous crowd in the street below, 'Long live George Washington, President of the United States!' while children shouted for joy and old men wept at the significance of the occasion."
 United States Government Printing Office. "Constitution of the United States of America, Article 2, Section 1." 1938. Washington, D.C. Page 26.
[2-3, 4] Richardson, James D. "Messages and Papers of the Presidents," Volume I, 1897, Bureau of National Literature, Inc., New York, Page 34-35.
Portrait of Charles Thompson. http://contemporarymakers.blogspot.com/2011/05/american-revolution-patriots.html
Two Dollar Bill. http://www.icollector.com/1976-2-Star-Note-Two-Dollar-Bill-Note-G-Mint-Chicago_i9545338
Portrait of President George Washington) http://www.thefamouspeople.com/profiles/george-washington-18.php