This is basically for my brother, as it came up this past weekend and I missed my chance to make this point. But I'll make it in public because... well, what the hey. And perhaps someone else might want to jump in, too.
So, I only know of four basic methods for assessing the value of a share of stock, and they all require that you guesstimate some crucial value. But despite that, they are all useful to know and use:
 You can try to assess the liquidation value of the company. If the company were to cease business today, and have all of its assets auctioned off, what would be left after paying off its debt? Okay, and how much would that be, per share? That's the pershare liquidation value. This value is conceptually straightforward, but not as simple to calculate as one might think. The tricky part is to determine what the nonfinancial assets are worth. If the company is a manufacturer, for example, what is the back stock worth? The unused raw ingredients? The machinery and the plant? How about the patents and other IP? This method takes a lot of domainspecific knowledge to accurately estimate, and so I don't use this method very often. However, I'm told that one can come close to this value by using 'book value per share' (BVPS), a standard value on many financial sites.
It used to be the case that one could find stocks selling for below BVPS, and one still can. These days, however, such companies are usually in deep, deep trouble, and just might be auctioned off tomorrow. If a company is selling at or below BVPS, I would be deeply, deeply suspicious. After all, BVPS doesn't take into account the economic value of what the company is doing with those assets the company's 'value add', as it were. But still, one can use BVPS as a sanity check, a lower bound on the value of a company, or a measure of how much of a company's value is tied up in assets such as commodities or real estate.

Another, more theoretically valid measure, is called the net present value valuation. Suppose that I had a magic box that would produce one dollar per year, in perpetuity. What would that box be worth today? Well, it would be the sum of:
 This year's dollar, which has the present value of one dollar.
 Next year's dollar, which must be discounted back to present value. What is that? Suppose interest rates are 5%. How much must I put in the bank now, to get one dollar next year? $1 / 1.05 = 95 cents, about. So next year's dollar has a present value of 95 cents.
 The dollar of the year after that, which must again be discounted back to present value. $1 / 1.05 / 1.05 = 91 cents.
 And so on.
If you write out the first few terms of this sum, you realize that you're summing a geometric series. You go look up the formula, plug in the numbers, and get a valuation of $21.
Of course, it isn't quite this easy to use this method to assign values to companies. The amount of free cash they generate (you want to use free cash flow, not profit) fluctuates from year to year, and it's hard to forecast. Likewise, interest rates are bot crucial to this calculation and hard to predict. So while this method is theoretically accurate, it doesn't tend to be very useful in practice.

Then there is what I call the 'greater fool' method of stock pricing. What is a stock worth? What someone will pay for it. That's really hard to predict in the short run, however, since people are irrational in the short run. But if you are willing to be patient, and the company has fairly steady performance, you can try to predict a 'baseline' price that should come to pass when people come to their senses a few years from now:
 Find a company that has exhibited steady, predictable earnings growth for the past 10 years. You're looking for a company who was grown earnings by roughly the same percentage every year since 2000. Yes, they exist.
 Using that historical growth rate, and current earnings, extrapolate out to five years from now. Now you have a predicted EPS for 2015.
 Looking back 10 years again, find the average Price/Earnings ratio.
 Multiply your predicted 2015 EPS by this historical P/E, and you have a sane predicted price for 2015.
 Discount that price back five years, to the present, using the rate of returns you would like to have. Boom: you now know what current price you should pay for a share of that company's stock.
Again, this method requires that you predict the future. Therefore, it is best to incorporate a 'margin of safety' to this calculation somewhere. One approach (which learned about from Phil Town) is to perform this estimate as accurately as you can, and then simply apply a 50% 'margin of safety' discount at the end. Another approach (which I learned about from Charles Mizrahi) is to instead use very conservative estimates for EPS growth and P/E. I use both of these methods, and then believe whichever one comes in lower.
 Lastly, one can use the 'earnings power value' (which I learned about from Bruce Greenwald). Suppose that a company earns $1 per share. How much is that share worth? In this method, you completely ignore the future and simply ask yourself: how else could I make a dollar off of that company? Well, you could lend money to that company. Okay, so how much would you need to lend to the company to make $1? That depends on how much interest the company needs to pay to borrow money, also called the 'cost of capital'.^{1} Suppose that the company can borrow money at 5%. Then you would need to lend them $20 to make $1 over the course of the year. Ergo, a share of that company is worth $20, and this is called the earnings power value (EPV) of a share.
The tricky part here is to determine the cost of capital for a particular company. If there is a web site which will compute this for me, I haven't found it yet. The difficulty is that companies can have long and shortterm debt, and these will be at different rates. What to use? I end up not even bothering. Instead I calculate the EPV for a range of reasonable costof capital rates and see how those compare to the current share price.
Okay, so let's run the numbers:
 A share of Apple (AAPL) is $325.
 The BVPS of Apple is only about $52.
 Phil Town would note that they have grown EPS by 45% per year over the past five years, that they currently have an EPS of $15.15, and their average P/E for the past five years has been about 21.5. So he would estimate their stock to be worth about $3161 in 2015. But he applies a 50% marginofsafety discount, so that would become $1580. That implies a rateofreturn of about 32%. Amazing, but don't get excited just yet.
 Senor Mizrahi, using much more conservative values for EPS growth and likely P/E, estimates that Apple will be selling for $436 in 2015. This means a rateofreturn of 6% over the next 5 years. Not shabby, but not great. More to the point, no better than my cost of capital.
 Given that EPS is $15.15, we get a pershare EPV of:
 $505, for a 3% costofcapital rate,
 $378, for a 4% costofcapital rate, and
 $303, for a 5% costofcapital rate.
So, Apple is overpriced according to liquidation value, reasonably priced according to the EPV method, and reasonably priced according to my 'greater fool' estimates. (Remember, I use the lower of the Town and Mizrahi numbers.) It was a great buy in 2009 (most of these estimates would have been roughly the same then) but now it seems like an average one.

Side note: this rate is also a good baseline for how much profit a company needs to make to be worthwhile. Suppose that a bank has $100 in equity, and can borrow money at 4% If that company does not make at least $4 over the year, then they would have been better off liquidating themselves and lending out the $100 they would have made! If a company can't beat the cost of capital, then they have been forced by the market or competition into a sort of equilibrium. Rephrased, they have no competitive advantage. ↩