At this site you can check out Jefferson's first inaugural, plus the two preceding drafts of it as well as an editorial note.
I thought some of the information on inaugural day was interesting:
The morning began with a discharge of cannon from the company of Washington artillery, and at 10:00 the Alexandria company of riflemen joined them to parade in front of Conrad and McMunn’s boardinghouse, on New Jersey Avenue near the Capitol, where Jefferson was residing. At noon, dressed as “a plain citizen, without any distinctive badge of office,” the president-elect walked up Capitol Hill for the ceremony. Unlike his predecessors, he wore no ceremonial sword. Joined by a number of his fellow citizens and members of Congress, Jefferson was preceded by a detachment of Alexandria militia officers, swords drawn, and by the marshal and deputy marshals of the district of Maryland. When Jefferson arrived at his destination, the officers opened ranks and saluted. Another discharge of the artillery was sounded, and he entered the Capitol. Members of the House and Senate rose to their feet in the Senate Chamber, a large semicircular room with an arched roof and spacious gallery. Senators sat on one side of the chamber, and the other was given over by the members of the House to the women who were in attendance. Aaron Burr rose to relinquish the chair of the presiding officer of the Senate, which he had temporarily occupied, to Jefferson. After a short pause, Jefferson stood to deliver his speech in a room that was, Margaret Bayard Smith claimed, “so crowded that I believe not another creature could enter,” and that according to newspaper reports held the “largest concourse of citizens ever assembled here.” The Aurora reported an audience of 1,140 (of whom about 154 were women) in addition to members of Congress. After delivering his address in “so low a tone that few heard it,” Jefferson seated himself for a short time and then proceeded to the clerk’s desk to take the oath of office, which Chief Justice John Marshall administered. The artillery salutes resumed, with 16 rounds fired by the Alexandria artillery company from two field pieces brought specially from their town for that purpose. The citizens responded with 16 discharges from a 6-pounder that was positioned just below the town. Jefferson and the procession returned to Conrad and McMunn’s, where he was again saluted. Foreign ministers, members of Congress, and residents of the District of Columbia who had come to pay their respects awaited him. Other inhabitants of the nation’s capital assembled to call upon Vice President Aaron Burr, who also received a 16-gun salute. A final display of firepower ended the evening, and the Alexandria artillery company crossed the Potomac to return home.
I thought I'd quote a little of the finished document here for you:
During the contest of opinion through which we have past, the animation of discusions and of exertions has sometimes worn an aspect which might impose on strangers unused to think freely, and to speak and to write what they think; but this being now decided by the voice of the nation, announced according to the rules of the constitution all will of course arrange themselves under the will of the law, and unite in common efforts for the common good. All too will bear in mind this sacred principle, that though the will of the majority is in all cases to prevail, that will, to be rightful, must be reasonable; that the minority possess their equal rights, which equal laws must protect, and to violate would be oppression. Let us then, fellow citizens, unite with one heart and one mind, let us restore to social intercourse that harmony and affection without which liberty, and even life itself, are but dreary things. And let us reflect that having banished from our land that religious intolerance under which mankind so long bled and suffered, we have yet gained little if we countenance a political intolerance, as despotic, as wicked, and capable of as bitter and bloody persecutions. During the throes and convulsions of the ancient world, during the agonising spasms of infuriated man, seeking through blood and slaughter his long lost liberty, it was not wonderful that the agitation of the billows should reach even this distant and peaceful shore; that this should be more felt and feared by some and less by others; and should divide opinions as to measures of safety; but every difference of opinion is not a difference of principle. We have called by different names brethren of the same principle. We are all republicans: we are all federalists. If there be any among us who would wish to dissolve this Union, or to change its republican form, let them stand undisturbed as monuments of the safety with which error of opinion may be tolerated, where reason is left free to combat it. I know indeed that some honest men fear that a republican government cannot be strong; that this government is not strong enough. But would the honest patriot, in the full tide of successful experiment, abandon a government which has so far kept us free and firm, on the theoretic and visionary fear, that this government, the world’s best hope, may, by possibility, want energy to preserve itself? I trust not. I believe this, on the contrary, the strongest government on earth. I believe it the only one, where every man, at the call of the law, would fly to the standard of the law, and would meet invasions of the public order as his own personal concern.—Sometimes it is said that man cannot be trusted with the government of himself. Can he then be trusted with the government of others? Or have we found angels, in the form of kings, to govern him? Let history answer this question.
Jefferson's speech set a precedent that subsequent presidents would follow:
Departing significantly in form and substance from those of his two predecessors, Jefferson’s First Inaugural Address established the formula that was used by all American presidents until Lincoln. The nation’s third president avoided specific mention of issues of policy or reference to the partisan nature of the election and emphasized abstract political concepts that all could embrace (Jeffrey K. Tulis, The Rhetorical Presidency [Princeton, 1987], 50). While his interpretation of fundamental republican principles in fact meshed nicely with the policies of the Republican party, his conciliatory rhetoric brilliantly embraced both parties by describing a single nation, one that the heroes of the Revolutionary generation would recognize and approve. In his revised draft, in fact, he made a pointed allusion to George Washington, the “first and greatest revolutionary character, whose preeminent services had entitled him to the first place in his country’s love.” In delivering his first public message to the country as president, Jefferson sought the mantle of the father of the country to lend legitimacy. But as he drafted the address, Jefferson also asked himself, “is this exactly in the spirit of the patriarch of liberty, Samuel Adams? is it as he would express it? will he approve of it?” (TJ to Samuel Adams, 29 Mch.). Jefferson’s brilliance lay in being able to encompass in his Inaugural Address the ideals of Samuel Adams and George Washington, finding room for both within the political spectrum of the republicanism of the Revolution.