How The Primary System Works
The primary system is run by the individual political party's. You must either vote all Republican, or all Democrat, which are the two major political parties of the United States. For each state a candidate wins, they are awarded delegates. Each state has a certain number of delegates, which are based on population. For the Democrats it works like this in almost all states.
Obama wins 60% of the popular vote in State X -> Obama get 60% of State X's delegates.
However for the GOP/Republicans it works like this in almost all states.
McCain win 51% of the popular vote -> he get's all the delegates.
There are also 400 "super delegates" between all the states that can go to any candidate. Each state has a set number of super delegates. This will probably be the deciding factor between Obama and Clinton.
The November Election
After the primaries are all done, one candidate from each party will be left standing. They will run against each other in the November 2008 election. This election is only one day, and not spread out like the primaries are. The winner in November will become the next President of the United States. They are sworn in on the 20th of January. (Hence the bumper sticker that just says 1/20/09, it's the date Bush is no longer President.)
In the November election each state once again has a set number of delegates. However, in almost all of the states which ever candidate gets the most votes gets all the delegates. There are a few "split states" where the delegates are divided. There is a problem with this system. Because the winner is based on delegates, not the popular vote, it is possible to have lost the popular vote, but still have won with the delegates like George Bush did in 2000 when he ran against Al Gore.
What Happened to Michigan and Florida
For the Democrats, Michigan and Florida's primaries didn't count at all. The the Republicans, only half the delegates were up for grabs. This is because both Michigan and Florida "broke the rules" and did not formally change the date of their primaries. They just moved them. The political parties punished the states for this. In the November election, the states will still get their full number of delegates.
All of the Democratic candidates removed their names from the ballots in Michigan and Florida, except for Hillary Clinton. Apparently, she didn't meet the deadline for removing her name. Some speculate she purposefully did this, and will attempt to reinstate the delegates, because she was the only candidate and therefore won. However, Hillary did not get the entire vote, because many Democrats went out and voted "uncommitted." If enough people vote uncommitted, uncommitted delgates will be sent to the convention where the winner is decided that can go to any candidate. In theory, these would go to Obama.
General Public Opinion
Our system is way screwed up, and should be changed.