I guess I didn't get a lot out of Tichfield's links... but the process is fairly straight forward at least to those of us who live here.
Once each four years we have a Presidential election. It coincides with some Congressional elections as well (I'm describing national elections as opposed to State). The two major parties, Democrats and Republicans will begin putting forth their various candidates over the year preceding the actual election. They will go through either caucus' such as in Iowa last night or primaries such as the upcoming New Hampshire vote in about a month. In those, the candidates try to get as many votes as possible which actually translates into delegates commited to him or her. Sometime in the late summer (the National election is the on the Tuesday following the first Monday of November) each Party will hold its respective nominating conventions at which time the various delegates vote for their candidate. This process can become confused if there are no clear cut early winners, but somehow, a Presidential candidate emerges from each party. He (or possibly she) the chooses the Vice-Presidential running mate and the real campaign begins in earnest, resulting in election on the date as described above. After the candidate is elected, they are sworn into office by the Chief Justice of the Supreme Court on January 2 of the following year. Senators and Representatives may be elected as well, but their terms may not coincide with the Presidential election, (Representatives are elected for 6 years, Senators for 4). In a nutshell...