A page of politics, focusing on the U.S.A., since that affects me most. For personal influence, the most important offices are municipal, so these go from the local outwards.
Here in Tucson, Pima County, Arizona, the most important governing bodies are the school board, the mayor & city council, the county board of supervisors, and state legislature (not that the governor should be sneered at). These are filled by city, county, and state elections; the county has a jurisdiction search. Always keep up with your local government and state news.
At the federal level is the federal judiciary headed by the Supreme Court; the U.S. Congress, consisting of the House of Representatives and Senate; and the President. As chief executive, elections of the latter are considered particularly important. In theory, I have more influence with my congresscritters, Rep. Ron Barber, Sen. John McCain, and Sen. Jon Kyl; you can find your own, read their biographies, or check out the Congresspedia. This is all built on the Declaration of Independence and Constitution; for interpretion help, read comments from the framers, annotations based on decisions of the Supreme Court who use them on a daily basis, and the legal code that Congress passed under their authority.
Unlike the individual states, the federal (not national) government has no home page—for starters, try USA.gov, FedWorld, GovSpot, or this directory of federal agencies— and for general news, FedNet. At least there's a U.S. Government Manual. And while it looks large at first glance (check out the budget, debt, and other useful statistics), that's because it provides many useful services, such as weather forecasts (NWS), recent earthquake and seismic hazard information (USGS), space pictures (NASA), census data and quick facts (Census Bureau), public health information and alerts (CDC), international travel advisories (State Department), copyright (Library of Congress) and patent & trademark (USPTO) protection, and our national parks and forests—not to mention some official propaganda (available in RSS).
To find out what the major players on this stage are after, read the platforms of (from left to right) the Green, Democratic, Republican, and Libertarian parties. For elections information, The Green Papers is good; try this daily political briefing for (protected) news of what happens in between. Various organizations score office holders by agenda; the results are collected by Voter Information Services. Other useful groups include Project Vote-Smart, Political Money Line, Open Secrets, Common Cause, Public Agenda Online, Institute for Public Accuracy, Center for Public Integrity, Annenberg Political Fact Check, National Priorities Database, and This Nation. This portal of resources is also worth noting.
This system is structured by laws—for assistance, see the Law Reference Desk, Law Library of Congress, World Law, or more World Law; for voting, see Election World and this guide to organizing elections. If you're concerned about who your dollars support, you may want to check Buy Blue before spending them. For help changing things, try Protest.net, Working for Change, Move On, ACLU, AFSC, ZNet Social Change, Antiwar.com, and Nonviolence Web. Be careful: know how to perform civil disobediance and nonviolent action. There's also info on my national and state Green parties, and a list of Greens in office.