Politics has a language all its own.  Like most academic subjects, the basic terms are understood by everyone in the know, and the rest of it is debated hotly.
When you’re done reading this, you should have a basic idea of what the political spectrum is, as well as how to understand and use the terms associated with it.  You should also have a fair idea of where people stand on corresponding economic and social spectrums.
So let’s do this . . .
THE POLITICAL SPECTRUM
WAY back when, during the French Revolution in the 18th Century, representatives sat in the French National Assembly based on how they felt about things politically.  They sat in a big semicircle around the chair of the Speaker (the person running the Assembly’s meetings).  If they loved the King of France, really liked things just the way they were, and didn’t really want things to change, they generally sat to the right of the Speaker’s chair.  On the other hand, if they hated the way things were and wanted to change how things were, they sat to the left of the Speaker’s chair.  And if people really weren’t sure where they should be, or if they didn’t have any real issues about change, they sat in the center (the middle) between the people on the left and the right.
We’ve taken the basic political spectrum from the French and the way they sat.  Basically,
It’s all about how people feel about change.
So the political spectrum looks like this:

Moderates

Liberals

Conservatives

Moderates are in the middle of the spectrum, as you can see.  They either don’t know where they stand, or don’t care, or have an attitude about politics that tries to take from both sides of a given issue.
The farther to the left one goes on the spectrum, the more one likes change.  So people on the left side of the spectrum are generally known as liberals.  That’s all the word means—if you think change is a good thing in general, you’re a liberal.  To get the change they want, they operate within the government to get it—they call or email elected officials, they hold marches or protests, they give money to political candidates, and they vote for people who support the kind of change they want.
The farther to the right one goes, the more one doesn’t like change.  Those people are generally called conservatives.  There’s a little more to this definition, though—they also generally want things to go back to the “good old days” that they think were better than today.  Like liberals, they are law abiding about preventing change—they go about preventing change or “turning the clock back to the good old days” through legal means.
To reiterate: the farther to the left or right you are, the more you either like or dislike change.
But there are some groups that are way more to the left or right of conservatives or liberals.  On the political spectrum, they are here:

Conservatives

Moderates

Liberals

Radicals

Reactionaries

Generally speaking, radicals want extreme change, and they wanted it yesterday.  They also operate at times outside the law to get what they want—whether it’s nonviolent protests that break a law, acts of violence or vandalism.  Communists, anarchists, the Weather Underground, the Animal Liberation Front, and Greenpeace (back in the day when they sailed ships into nuclear test sites to try to stop detonations) are all examples of radical groups.
Reactionaries are just as extreme, only in the opposite direction.  They want to go back to the good old days now, or they hate change so much that they’re willing to do just about anything to stop it.  Like radicals, they don’t have a problem resorting to illegal acts to meet their ends.  Protesters blocking women entering abortion clinics (or bombing the clinics themselves), anti-government extremists like the late Timothy McVeigh, neo-Nazis, the Ku Klux Klan, the White Aryan Resistance, or similar groups are all examples of reactionaries in the United States.
It’s important to remember that there are far more liberals, moderates, or conservatives than radicals or reactionaries.  Radicals and reactionaries are also called fringe groups, since they’re so far outside the mainstream of American political culture that they attract very few people.
So where do the two major political parties fit on this spectrum?  For no particular reason, let’s start with the Democrats:

The Democratic Party

Liberal Democrats

Moderate Democrats

Conservative Democrats Democrats

They have their moderates, their liberals, and their conservatives, as you can see.  Their numbers inside the party change, but the party leadership and people they elect to Congress have largely been liberal or moderate Democrats.  

Conservatives

Moderates

Liberals

Radicals

Reactionaries

Dems Democratic Party

L.Dems

M.Dems

Con.Dems

Compared to the rest of the country, they are roughly here on the general political spectrum:

…and the dotted lines indicate where each Democratic group falls on the general spectrum.  Notice how liberal Democrats are much more liberal than typical liberals are, how moderate Democrats are more liberal than moderates are, and, well, how conservative Democrats are more liberal than moderates overall.  These are estimates of where the Democrats are, and exactly where they are is open to debate.  You could make a good argument that John Dingell (D-MI), a conservative Democrat, is actually to the right of ‘moderate’ on the spectrum, although his recent commercials might contradict this.  In an election year like this one, it’s harder than usual to figure out where politicians stand.

The Republican Party

Liberal Republicans

Moderate Republicans

Conservative Republicans Democrats

Now, the Republicans:

Conservatives

Moderates

Liberals

Radicals

Reactionaries

Dems Democratic Party

L.Dems

M.Dems

Con.Dems

GOP

L.Rep.

M.Rep.

C.Rep.

As you can see, they have their liberals, moderates, and conservatives, and they fall on the general spectrum in the obvious places:

…and, as you can see, they’re more conservative than the Democrats, although it seems like Republican party leaders are moving further to the left, having been spanked in the 2006 elections.  Exactly how far is open to interpretation and debate (you could make a good argument that there is almost no difference at all between liberal Republicans and conservative Democrats), but Republicans have generally been more conservative than Democrats.
ISSUES, POLITICAL PARTIES, AND THE SPECTRUM:

Conservatives

Moderates

Liberals

Radicals

Reactionaries

Dems Democratic Party

L.Dems

M.Dems

Con.Dems

GOP

L.Rep.

M.Rep.

C.Rep.

Since Democrats are generally liberal and Republicans are generally conservative, one can pretty easily take issues and figure out where liberals and conservatives, Democrats and Republicans stand on them all.  Here are a few examples, placed relative to the spectrum:

Role of Government	
More
Government	Less Government	
Crime	
Rehabilitation	Punishment	
Gun Control	
More	Less	
Abortion	
“Pro-Choice”	“Pro-Life”	
Taxes	
More on wealthy	Less on wealthy	
Same-Sex Marriage	
For	Against	
The War on Terrorism	
Engagement	Pre-emption	
The Iraq War	
Withdraw	Stay	

There are also plenty of issues that don’t fall neatly between opposite sides of the spectrum.  One example is the future of Social Security.  Democrats might say that it needs to be expanded and funded more, and conservative Republicans might say that it needs to be handed over to private investors or dumped altogether, but the huge numbers of elderly people on Social Security in the United States (and the fact that they vote in far larger numbers than everyone else) means that neither party is going to touch the program in the near future if they want to stay in office.
And there are other issues that the parties have completely shifted their positions on, making it difficult, if not impossible, to place them on the spectrum.  One of these is spending.  Republicans, for example, are for less government spending—although from 2001-2006, there have been record budget deficits (where the government has spent a lot more than it receives in revenue) with Republicans running Congress and a conservative Republican President.  They might tell you that “9/11 changed everything” and/or “Reagan proved that deficits don’t matter,” but this is ideologically against what Republicans in the past have believed in.  
Democrats haven’t changed positions so blatantly in recent times, but on past issues they have done exactly the same thing.  The Civil Rights issue is the best example of this.  Democrats claimed that they were the party of the masses, but they took great pains to keep African-Americans out, and were some of the louder advocates of segregation.  Then they changed their minds, for the most part, in the late 1960s, and have since been quite the opposite.
Finally, many Americans have (or try to be) in many places at once on the spectrum, depending on the issue.  Look at the issues above, decide where you are on them, and you might find yourself all over the spectrum, depending on the issue.  You might also find yourself believing exactly what your parents believe . . . In fact, I’d bet that you already do 
THE ECONOMIC SPECTRUM

Moderates

Interventionists

“Liberals”

This whole economic spectrum is tied into one issue, the economy.  It’s not based on change; it’s based on the level of government involvement in the economy.  People on the left want more involvement, people on the right want less:

Moderates, here, are moderates.  They’re neutral on particular economic issues, or try to adopt compromise policies between different, competing interests. 
 Interventionists want the government to directly intervene in the economy to try to make it do what they want it to do (which is to try to equalize wealth between upper, middle, and working classes in their countries).  They mostly do this through a lot of regulation, taxes, tariffs, and spending.  Socialists are big on this position.  Interventionists believe that free markets are generally unfair—where the rich get richer and the poor get poorer—and that government regulation is necessary to enforce both fair deals and fair results for everyone.
Economic “Liberals” are actually political conservatives (and they call themselves “Liberals” because the economist who made most of this up, Milton Friedman, called his position “liberal”).  They want the free market left alone by the government, so individuals can make whatever economic choices they want and everyone ends up benefiting because everyone gets what they want for the lowest cost.
Issues on this spectrum are a lot more difficult to pin down.  Take globalization, for example.  Economic “Liberals” might love it, but don’t like the World Trade Organization’s regulation of it.  Interventionists might hate globalization for its own sake, but support the WTO trying to keep things fair.
Or that’s the ideas they have, at least . . .   We’re still arguing about all of this, and probably always will.
THE SOCIAL SPECTRUM:
The social spectrum is quite simple.  It deals with the relationships between individual people and as a whole.  Like the political spectrum, it’s all about change:

Moderates

Liberals

Conservatives

…and it falls pretty much on the same lines as the political spectrum.  Social liberals are for social change—change for the better, not necessarily for its own sake.  Social Moderates, as always, either don’t know, don’t care, or are in the middle of a given social issue.  Social conservatives can also be called “traditionalists,” because they either don’t want social change, or they long for those good old days when things were ‘better’ than they are today.

IN CONCLUSION,
The spectra discussed above are the basics.  Political scientists argue hotly about them, and have even introduced other spectra that complicate things a lot more, in order to try to nail down why people believe as they do politically, economically, and socially.  But people are definitely variables, and as Einstein said, “Politics is harder than physics.”  But if you understand what’s here, you’ve come a long way to understanding the basics of politics, particularly American politics.