So, how and why did it all begin?

In ancient Greece, they often combined religious festivals with sporting events, to honor certain gods.  The Greeks held the following: The Pythian Games
The Nemean Games
The Isthmian Games
The Olympic Games

 It was the last one, the Olympics, that were held for the Greek God Zeus and were also the most popular with the people. The first game is said to be held at Olympia, Greece in 776 B.C. and has been held every 4 years since = 1,168 years!

Then, Greece came under the rule of the Roman Empire and the Olympic games were declined, to the point where they actually declined in 393 B.C. by the Christian Roman Emperor, Theodosius I, who objected to what he felt were some "pagan rites" associated with the games.

In the beginning, the Olympic games were confined to just one day and one event.  That event was a footrace that was the length of the stadium.  Soon, additional races were added as the popularity grew, as well as discus and javelin throws (tosses), broad jumps, boxing, wrestling, chariot racing and a pentathlon.  The pentathlon was composed of 5 different track and field competitions.

I guess for those who weren't so physically athletic, they also included competitions for poetry, dramatists and orators.

Soon, the length of the games extended to 5 days and the winners (often like today) were celebrated and considered national and local heroes.

Baron Pierre de Coubertin of France, and educator and scholar wanted to discourage professionalism in sports by holding amateur world championships.  As a result, he's the one who is credited with reviving the Olympics as we know them today around the late 19th century. 

The first Olympiad of modern times was held under the King of Greece in 1896 in a new stadium built for the purpose of Athens.  Since that time, the games have been held in cities all over the world at 4-year intervals, with an exceptional lapse during World War I and World War II.

It wasn't until 1924 when the Olympics became seasonally separated into the Winter Olympics and the Summer Olympics.

Today's modern Olympics are normally set at resorts for the Winter games and in large cities for the Summer games. And to help hosting cities prepare, in 1994 the 4-year cycle became split where the games were 2 years apart between the seasons.  An example is:
Winter Games in 1994 and and 1998, but the Summer Games in 1996 and 2000.

The Summer Olympic Games have right now 23 approved sports including archery, basketball, boxing, conoeing, cycling, equestrian, fencing, football (aka soccer), gymnastics, modern pentathlon, rowing, swimming, diving, volleyball, water polo, weight lifting, wrestling, and yachting.  The newest summer sport of synchronized swimming was added due to popular demand.

The Winter Games include biathlon (skiing and shooting), bobsledding, ice hockey, luge, ice skating (figure and speed).  During the last winter Olympics in 1998, winter snowboarding was accepted as an official winter competition.

About 160 countries compete and send thousands of athletes (male and female) to the Summer Olympics.  The Winter Olympics are smaller as far as nations sending athletes.  They have about 60 countries that participate.  Countries that have an environment that fits a sport usually dominates a sport.  But sometimes a country will challenge traditions.  One good example was the Jamaican Bobsled team.  Although it had no snow to practice, and it came in last, it won the hearts of the world with it's sincere efforts.

Television (and especially color!) has increased the popularity of the Olympics worldwide.  And in some ways has also been the cause of it's commercialism that some complain about, often resulting in what some consider "prejudicial judging" because the common pattern is that only the medal winners (esp. those with the Gold) get offers for commercial product endorsements and potential financial earning power in their futures.