Imagine a footrace between several people. That would be the simplest model of a race. The tour is incredibly more complex than that. There are no only individuals, but teams. Some riders are not there to win themselves, but to be supportive of others on their teams. Quaintly, supportive riders are called "domestiques."
Secondly, it is cumulative, so that the winner is not the first across the finish line, but the rider with the lowest overall time at the end.
Most riders, most of the time, are in a huge pack called the "peloton," riding very close together. It is a very gregarious event. The leader of the race, wearing the yellow jersey, is often to be found in the middle of the peloton. There is no particular advantage to being at the front of the pack, since only a few second separate the front from the back.
Riders stage escapes or attacks by trying to separate themselves from the peloton, usually in small groups. The maillot jaune and other top riders can tolerate an attack if it doesn't include serious rivals. The leader himself can attack, and if he is successful put some distance between himself and key rivals, since not all the rivals will be part of the escaping group. After an attack the peloton as a collective entity can try to catch up with the escaped riders. There is a cost in an escape: if unsuccessful, it is a loss of valuable energy. There are also huge gains to be made if a rider escapes and moves up in the overall standings. Most days are not decisive, but some are, with a dramatic escape that changes the standings. The mountains, first the Pyrenees and then the Alps, are the most decisive, because they tend to spread out the riders more and allow from more drama than the flatter parts of the race.
Riders can always win glory in individual stages, but most are out either to win the whole thing, be a domestic servant, or vie for one of the secondary prizes like "king of the mountain."
It's hard to get too enthusiastic because even Armstrong, who passed every drug test ever, is now under suspicion of doping.
Most of the time, then, you want to be in the peloton, more or less following the status quo. You want to have some individual distinction, but you can also be part of a team. Daring escapes are cause for excitement, but are risky and not always successful.