From my limited experience with foreign exchange... Money is a commodity.. people buy it and sell it like other products.. if "money" is in demand the price goes up.. this is the case when a countries stocks are hot, and you need to purchase that countries currency to buy that stock... I've also seen the currency rise on news and speculation. Many years ago, I administered foreign receivables... My job was to settle letters of credit from Britain... I remember on one ocassion Margaret Thatcher said something to upset the markets.. her remark caused the price of the UK pound to fluctuate.

Q: How do currency markets work?

A: The FX (foreign exchange) market works very much like the stock market where potential buying parties bid $Y of country 1's currency to buy $1 in country 2's currency. Potential selling parties sell (ask) $1 of country 2's currency for $Y of country 1's currency. Like the stock market, there are also a swaps, futures and options in this market.

Q: What factors are behind why currencies go up or down?

A: Just like any open market, currencies go up and down based on supply and demand. Many factors affect the supply and demand of a particular currency. Some were listed well by the other posts.

Q: What roles do governments, central banks, institutions, and traders have in the process?

A: It's common practice that gov'ts intervene to "control" the value of currencies. For example, although it's not general public knowledge, the Canadian gov't is actively purchasing up US dollars in the FX market in an effort to stop the US/Canadian exchange rate from dropping further. This has dramatic economic consequences for the Canadian ecomony if the Canadian dollar were to strengthen too far and too quickly.

The fiat currency is the basis for currency markets - that is, currency that is not made of precious metals.

The factors that influence what the value of a fiat currency are the state of the country's economy, what the gov't says the value should be, their fiscal policies, as well as what the currency is trading at.

And what the currency is trading at is a product of these factors as well as the typical factors which would affect any stock trading. eHow has a great outline, here, which describes them.