The mysterious Bob requested a short "course" on how fiat money works. Considering that our economy runs on fiat money and probably less than 1% of Americans understand it, it's probably important to come up with a simple way to wrap one's head around it.
Imagine we all live on an island, isolated from the rest of the world. (This keeps things simple; we'll talk about international trade later.) People on the island obtain goods and services by trading with each other. Whatever merits this system has, it can be very tedious to enter into a transaction. For example, if you're a calculus tutor and you want some salmon, you have to find someone who has a bunch of salmon and wants calculus tutoring. What are the odds of finding that person in a reasonable amount of time?
So the government of the island issues green pieces of paper called "dollars" and lets people trade with dollars. There's just one problem: These pieces of paper have no intrinsic value, so there's no way I'm giving you some of my stuff in exchange for dollars.
Now let's add one more kink that will actually make these dollars valuable. At the end of each year, every island resident (government worker or otherwise) has to pay a tax of $5000. These pieces of paper will be collected and tossed into a shredder. [Alternately, the taxpayer can simply submit a YouTube video of himself shredding the money he owed.] If anyone fails to turn in $5000, he'll be put out to sea in a raft with nothing but a DVD player with Britney Spears videos and "What's Happening!!" reruns.
Now no matter what you think of the idea of having a "head tax", you have to agree that dollars now have some serious value. They're the only form of payment that the government will accept for tax liabilities.
So now dollars have value and people can use dollars for trade. I can buy fish in exchange for dollars because either the fisherman needs the dollars to pay his taxes, or he knows that somebody else needs them for taxes (and thus that guy will trade for them).
One last problem we have to address: Where do people get dollars from? They need to accumulate dollars in order to pay taxes each year, after all. Saying that they get dollars from trading with other people is a cop out, because those people need to get dollars from somewhere. Even if somehow people "started out" with a certain number of dollars floating around, they will eventually be destroyed at a rate of $5000/resident/year.
The answer is that dollars can only come from one place: the government. The government can create and destroy dollar bills and they're the only ones who can do it.
So the island government decides to hire people to do various jobs around the island such as cleaning seaweed off the beach, maintaining the roads, and running a tropical counter-terrorism unit. The employees are paid in dollars. If the government wants to, it could even supplement the supply of dollars by dropping them from a helicopter and letting people find them.
So dollars "start" in the hands of people who sell their services (or goods) to the government, the dollars are used for trade, and they eventually end up in the hands of people who need to pay taxes (government workers or private sector workers alike.)
Now here's a good question to think about: How much does the government "need" to spend each year? As a follow-up, what happens if they spend more or less than that amount?