Well, I've been writing this off and on since 2009, and I've published previous bits of it in my last couple of diaries, which were a good long time ago. This time, however, I fully intend to release the entire thing whether or not I get any response, and who knows, maybe a potential employer will see it.
--Basic Overview of the Federal Government--
As we all learned in civics class, even if we forgot immediately after the test, the federal government is composed of three roughly equal branches. First, there's the executive, with power vested in the President (or if you're John Yoo or David Addington, all power, ever, is vested in him). Then there's the legislative, consisting of a House of Representatives elected by the people of the several states and a Senate elected two each from every state, originally by the state legislature but now by the people. Finally, the judiciary, consisting of judges who rule on the cases that come before them at various levels, from the local judge to the 9 Circuit Courts to the Supreme Court.
The legislative branch, as mentioned previously, is also called Congress, which includes both the House and the Senate, so saying "Senators and Congressmen" is stupid. The House currently has 435 voting members, set by statute - as opposed to the Constitution explicitly stating such. From 1789 to 1929, the House increased in size at every census, though not as quickly as the country was gaining population. At that point, they said enough was enough, and set the limit at 435 people, and so it's stayed since then (except after Alaska and Hawaii were admitted, when they just added two members to the House until the next Census), with the number of people each representative ... represents increasing steadily, though if a state gains one or more districts after a census, naturally the number of people per district decreases. Each member of the House is elected from a district drawn exclusively within one state, sometimes consisting of the entire state, as with Delaware, Alaska, and a few others. However, these districts are not restricted apart from needing to be close to the average population of a Congressional district (albeit sometimes 'close' is pretty ridiculously defined, as one Supreme Court case threw out a map with .14% difference in population between districts) and being wholly within one state, and many are disgustingly gerrymandered to favor one party over another. The Senate was originally elected by state legislatures, but during the late nineteenth century, legislatures were becoming increasingly less capable of agreeing on a candidate, with many seats remaining vacant for months or years. Thus the seventeenth amendment was drafted and passed, transferring the power of electing the Senate to the people of each state. Anybody who thinks that state legislatures are more capable of working together nowadays is delusional.
The president is elected by the Electoral College, which now consists of each state voting for the candidate who won the most people's votes in that state. Originally it was intended to be a deliberative, nonpartisan body that was selected by white men who felt those members could choose well. That didn't last past George Washington's reelection, with one voter complaining that the elector he selected was actually thinking instead of blindly going with his party. For several decades, each state chose its electors as it saw fit, using such methods as the current winner-take-all, having the legislature choose, having two votes go to the winner of the statewide vote and the rest apportioned by congressional district, drawing new districts with one vote each, and so on. After 1876, every state chose its electors by popular vote, and for almost every election since, the vote of the people of the whole country has corresponded to the vote of the Electoral College in outcome, though rarely in proportion. (A candidate who wins 58% of the popular vote will win a lot more than 58% of the electoral vote, and Perot's 19% in 1992 wasn't good enough for any electoral votes.) However, there have been a few notable occasions in which those have differed, most notably in 2000, when Al Gore won 500,000 voters more than George W. Bush, but Bush won 537 more voters in Florida, which had enough votes in the College to give him the election.
The federal judicial branch consists of judges in one hundred and eight courts selected by the President and confirmed with a majority vote by the Senate. These courts exist at three levels: at the top is the Supreme Court, which has nine justices (at the moment; there have been fewer in the past, and the number is set by statute, not the Constitution), and is the last resort, except for when one state sues another (which does happen sometimes), and those cases go directly there. Beneath the Supreme Court are the courts of appeals, which handle cases in their geographic regions, and set precedent for the same: for example, a decision by the First Circuit Court would strictly speaking affect only courts with jurisdiction over Maine, New Hampshire, Massachusetts, or Rhode Island. Again, precedents set by one court are not binding on the others, but may nevertheless influence their reasoning. Finally, there are the district courts, which exist entirely within states, and are assigned very roughly according to population (Ohio and West Virginia both have two, and Oklahoma has three), with each state having at least one court. Each judicial district has one district court and one bankruptcy court. If this seems boring . . . well, it mostly is (except for some of the district incongruities), but it's also a little important.