Here I go...
#1 Political parties are groups of people who generally share common ideals. They try to get candidates elected who share those same ideals. There are many parties besides the Democratic and Republican party; for example, the Green Party and the Libertarian Party. Also some candidates run as Independents, but if elected will usually caucus (meet to discuss ideas for legislation etc.) with one of the two current major parties (Democratic and Republican).
These ideals are usually codified in the party's "platform".
Democratic Party Platform
Republican Party Platform
Green Party Platform
Libertarian Party Platform
The political parties will often direct campaign donations to the candidates they think are most likely to win a particular seat, and/or run ads for them, and/or have people speak at rallies for them (Example: Former President Bill Clinton spoke at many rallies for Obama this campaign season, helping re-elect him.)
#2 Campaign headquarters are set up to solicit donations and act as a clearinghouse for information and response to opposing campaigns (replying to accusations made via either the news media or attack ads), and to coordinate volunteers to do things such as go door-to-door educating voters and asking them to vote for a particular candidate or make phone calls doing the same thing.
Obama national campaign site
Romney national campaign site
#4 Interest groups are groups of people who have a particular issue they want to see addressed. For example, anti-abortionists; pro-gay rights activists; business leaders; labor unions; advocates for the homeless; etc. These groups will often help campaign for candidates that they believe are most likely to favor legislation which will help their pet issues. In general, anti-abortionists and business leaders favor Republicans, while Pro-gay rights activists, labor unions and advocates for the homeless favor Democrats. These groups will sometimes make donations to political parties or candidates, make recommendations to their members regarding which candidates or parties they support, or endorse (approve of) a particular candidate (allowing that candidate to say that they've been endorsed by a particular group, which makes it more likely that someone who shares that group's ideals will vote for the candidate.)
Special Interest Groups and where they spent their money