What determines the price of a stock? Is it simply supply and demand?
Let's start by separating the question of the price of a stock from that of the value of a stock. It is often said that in the short term, the stock market is a voting machine. But in the long term, the market is a weighing machine.
When we're talking about the short-term voting machine mechanism of the market, we can see that many stocks momentarily get voted most popular, or prettiest, or most likely to succeed. The result of this daily "vote" on prices makes the price of stocks sometimes go quite high or low in a very short period of time. This daily voting mechanism is transient, however, and can be reversed the next day or the next hour. (A "bad hair day" for a stock, if you will.) That's why we Fools encourage investors not to pay too much attention to the day-to-day wanderings of stock prices.
However, when you stretch out the time horizon a little and look at the behavior of a particular stock over a longer period, such as five or 10 years, you can see that the change in a stock's price is determined by the weight of the accomplishments of the company rather than what trend may have momentarily caught the fancy of short-term investors. This ability of the stock market to accurately weigh things over time is what creates confidence in those investing their money in the market over the long term.
What determines the true value of a stock, as opposed to its price, is tricky. The value of any company is essentially an estimate of all the cash (including future earnings) that can be taken out of the business. Of course, cash that a company can earn this year is more valuable than cash that might be earned five years from now. So you must adjust estimates to assess the riskiness of the business and the time that it will take to make that expected pile of money.
Does the market do a good job of estimating those earnings and assessing the risks involved? Just as Winston Churchill famously said that democracy is the worst form of government except for all the other ones ever tried, so too it might be said that the market is the worst system for valuing businesses -- except for all the other systems ever tried.
As for supply and demand -- yes, they do count. When a stock price is falling with trading volume high, that is an indication that there is an increased demand to sell. After all, when a lot of people decide all at once to sell their stocks, that's going to show up as a large volume of trading. When people are really interested in getting rid of their stocks, they will accept much lower prices for their holdings than they did previously. Thus, the pattern you sometimes see of high trading volumes and falling prices.