Goomba or anyone else out there who doesn't know and cares:
Basic explanation:
President, head of state, head of military, generally in charge of making sure laws are carried out, has veto power over any proposed law which can be overridden by a 2/3 majority of the law making portion. Elected every 4 years.
House of Representatives and Senate, together known as congress. They write and then vote on the laws and are also in charge of the budget. 435 Representatives, and 100 Senators. Representatives are distributed among the states by population. Senators are simply 2 per state. A law to be put into action has to be passed by both the House and the Senate and then signed by the President. Senators are in office for 6 years with 1/3 of them being re-elected every 2 years. Representatives are simply elected every 2 years. Vice President also presides over the Senate and in the rare case of a tied vote, becomes the tie breaker.
The judicial branch is an odd one and slightly hard to explain clearly, but basically they're in charge of making sure that laws follow the constitution, and are able to strike down laws they deem not following the constitution. In that case the only recourse is for congress and states themselves to come together with large majorities and add a new part to the constitution. This doesn't happen all that often for obvious reasons, but the constitution as it stands has 27 amendments.
States are pretty much set up like this as well(numbers can vary though). Governors replace the president on the state level. States are considered able to govern themselves in matters not already covered by the national government.
EDIT: And I'm sure someone will find fault with this. It is simplified and doesn't cover everything, and large parts of it are off the top of my head, the oldest information is from a civics class 10 years ago. In any case there you go. Still, know this information and you'll probably know more than a majority of US citizens would know.
Edit2: Ah, yeah, the Electoral college system. Consists of a vote for each member of congress, plus 3 given to the people of Washington D.C. who don't really belong to a state and would otherwise not have representation. Each state is allowed to decide how they divide up the votes. Some are winner take all, others are proportional, and a few have different methods. In theory, each vote is up to the representative, and they don't have to listen to the people at all, but in practice they follow the rules the states set out which usually involves a state wide popular vote to determine how the votes will go. Because of these odd rules you can end up with a popular vote that's split near even and still have the electoral college be a landslide for one candidate. Or in some cases the winner might not even have the popular majority. It also puts special emphasis on certain states, generally known as swing states. These states are both divided, in that they're not a sure vote for one or another party, and also worth a good number of votes. There are a few that always seem to be swing states, such as Florida, and others that vary year to year.