Most of the events we today consider "Olympic" were not even labeled as such in 1900, often being called the "Championnats d'Exposition". Years later, many athletes did not know they had competed in the Olympic Games, believing that their sport had been only a part of the World's Fair. Only the athletics (track & field) events were really publicized in the media as being part of the Olympics.
The Games were stretched out over five months (May-October) and true opening and closing ceremonies were not held. It is difficult to know, because of the confusion over titles, and the many, many events held at the fair, what events should actually be considered "Olympic" and which should not. The IOC had no real control of this and thus one sees various listings. Many unusual sports and events were contested such as motorboating, balloon racing(/games/sportgames?editionid=2&sport_id=BLN), underwater swimming, and an obstacle swimming race.
The athletics caused a great deal of controversy. The French scheduled Sunday competition, which was not considered de rigeur in the United States in 1900. The Americans threatened not to compete and the French at first reconsidered, moving many of the events to 14 July. However, 14 July was Bastille Day, so the French moved the start of some events back to Sunday, 15 July. The Americans were confused by much of this, and many of them, notably several pole vaulters, failed to show for their events.
The star of the games was Al Kraenzlein, who through 2010 is still the only athlete to win four individual gold medals in track & field at a single Olympics. In the long jump, Kraenzlein met his arch-rival, Meyer Prinstein, a Jew. Both competed on Saturday, with Prinstein leading the qualifying for the long jump. The finals were to be held on Sunday and Prinstein refused to compete out of principle, although he had competed on his Sabbath. Kraenzlein did compete on Sunday and posted a winning jump that surpassed Prinstein's Saturday effort. Prinstein proposed a Monday jump-off, which Kraenzlein refused. Prinstein then punched Kraenzlein in the mouth and the two feuded for years.
Women made their Olympic début, with the first known competitors being croquet players and one yachtswoman, Hélène de Pourtalès. Charlotte Cooper (GBR) won the first championships by a woman, in tennis singles and mixed doubles. Margaret Abbott (USA) won the "Olympic" golf championship in early October. Neither of those two sports were labeled as Olympic by the organizers. Years later, Abbott's relatives did not know for certain that the title she won that day had been for the Olympic championship. Incidentally, in many sports, medals were not awarded. Most of the listed prizes were cups and other similar trophies. In several sports, notably fencing and shooting, professional events were held and considered later by the IOC to be of "Olympic" stature.
Of the 1900 Olympics, the best that can be said is that there was very little of true Olympic stature. The world awaited better, but it would have to wait for eight years.