The United States of America is a Federal Republic, not a democracy. Rather than the people directly governing, they choose representatives who govern on their behalf, thus "republic". The rules that govern elections were first established in the Constitution (ratified in 1789) and then amended periodically.
You must be at least 18 years old to vote (by Constitutional Amendment) on the first Tuesday in November of an even numbered year. If you live in a US state, you have 2 Senators, regardless of the state's population size. Each Senator had to be at least 30 years old when they were elected and 1/3 of the total of 100 come up for election every even numbered year. You can directly vote for each of them when their must stand for election every 6 years. Until the late 19th Century(?), Senators were voted in by state legislators.
You live in a single US House of Representatives district. Your Representative had to be at least 25 years old when they were elected and all 438 of them nationwide stand for election every even numbered year. As the population has been shifting towards the Sunbelt, each Census has resulted in more and more Reps coming from Sunbelt states and fewer from states losing population.
You don't vote for President, you essentially "indicate a preference". The President, minimum age of 35, is actually elected by the Electoral College, bunches of political party members who cast their votes around 6 weeks after Election Day. Each state gets a minimum of 3 members, 1 for each Senator and 1 for each member of the House of Representatives, so Wyoming gets 3 and California gets about 54 for a grand total of 538/- electors. Nearly all the states use a winner-take-all approach, so when a presidential candidate receives a majority of the votes from a given state, all of that state's electoral college members are obliged to cast their vote for that candidate when the Electoral College convenes. If one refuses, they are known as a "faithless elector". Two states, Maine and Nebraska(?) use proportional representation for their electors instead of "winner take all". Other states are considering this approach.
Debates endlessly rage about the merits and demerits of this system. For good and ill it has evolved into its current state over the last 222 years. I did not consult any notes, just going from memory here so feel free to chime in...
As for the impact of this system, political scientists have simplified the analysis of Presidential elections by labeling states as either "red", "blue", or "swing" (meaning neither red nor blue). A red state is expected to cast its electoral votes for the Republican candidate, a blue state for the Democratic candidate, and a swing state is up for grabs. Once the single Republican and single Democratic candidate face off after their respective party conventions at which they are formally designated as the candidates, the major focus is on the swing states as they try to win a majority of votes and thus all the electors in each of those states. Many of the "solid red" and "solid blue" states will be nearly ignored other than as sources of funds, volunteers, and other resources. e.g. California has been a reliably "blue" state for many years so the blue and red candidates will only briefly visit it a few times prior to election day. No semi-serious political scientist expects a Republican candidate to win California's electoral votes in 2012. Until another state is added to the Union (still a possibility - I'm lookin' at you Puerto Rico), the winning number is 270 electoral votes. The requirement only to win 270 electoral votes rather than the nationwide popular vote is why a number of candidates have become President without getting at least 50% of the nationwide popular vote (Bush in 2000, Clinton in 1996(?), Clinton in 1992, Kennedy in 1960(?), Wilson in 1912(?), Hayes in 1876, Lincoln in 1860(?). Most of these were caused by third-party candidates splitting the popular vote among more candidates. The two most contested elections were Bush/Gore in 2000 and Hayes/Tilden in 1876, both involving voting irregularities in Florida.
Here is a series of interesting red/blue maps from the 2008 election Maps of the 2008 US presidential election results
Now that you see how binary the system is, you can understand why people often feel they are forced to choose "between the lesser of two evils". Skip the lesser evils, Cthulhu for President 2012. Why vote for a lesser evil?