Methods for Stock Analysis
This is a general overview - additional research may be needed on each of the topics covered.
This is some surface-level research into the methods by which analysts gauge the potential future value of securities, as a method of actively managing a portfolio of stocks. The goal of these techniques is to assess the present value of a stock or predict the future value, as a means to determining whether a given security is a "good" investment choice.
It's worth mentioning that none of them are completely accurate and reliable, as even the best of predictive models is still just a model. Some dismiss all of this as hokum, with pretty sound reason.
Ratio Analysis
Ratio analysis examines the financial documents of a corporation and derives some standard ratios that can be used to assess the strength of a company, the changes in its capital structure and profitability over time, and the way in which it compares to competing firms.
For example, there is a "quick ratio" that divides current assets by current liabilities that assesses whether a firm has sufficient ready cash to cover its upcoming bills. From that, one can predict that a firm which is short on cash may be in a weakened financial condition and will soon run into problems and need to take on more debt ... though it may also be a temporary situation with a logical explanation (e.g. a retail store takes on a lot of inventory before the holiday season - so a snapshot in November would show an alarmingly low quick ratio, though it's likely that they will have a lot of sales in December and will be able to pay off their suppliers in short order).
More detail on this has been collected in a separate document - but the bottom line is that these are largely accounting measures that describe the present and past state of a company.
Trend Analysis
A separate method, technical analysis, looks at specific trends in stock prices (independent of anything to do with the company itself) as a method of predicting the future motion of the stock price.
For example, one can compare the current price to the average over time, with the expectation that a stock may fluctuate on a daily basis, but will not move more than a certain distance from its moving average.
In all, this is a slightly sophisticated way of expressing the expectation that a stock that has been rising in value will continue to rise, and one that falls will continue to fall. Or in other words, that the future performance will follow a predictable trend based on past performance. The fallacy of this premise should be self-evident.
Trend analysis can also be applied to measures other than price. For example, it can be applied to a ratio (such as a company's price-earnings ratio) for added complexity ... which would seem to compound the uncertainty of both methods.
Technical Analysis
Technical analysis uses statistics to predict the future price of a stock based on past performance. It seems to be a more mathematically complex approach to what is fundamentally trend analysis, as behind the numbers and equations, it is still a comparison of the current price to recent historical prices.
A common formula is (most recent closing price minus the low of the past 14 trading days) divided by (high of the past 14 trading days - low of the past 14 trading days). There are other stochastic models, that vary in their complexity (some can become extremely convoluted), but they essentially do the same thing.
This generally results in a ratio (0 to 100) where a stock is considered overbought (and bound to fall) if the value is over 0.8 and oversold (and bound to rise) if the value is under 0.2
This also generally results in a chart that tracks, very closely, the rise and fall of the price of a stock, much like a weighted average cost over time, so it's not terribly useful in predicting value in advance - it seems to suggest that a stock that is rising will continue to rise until it starts to fall.
Pattern Analysis
Pattern analysis eschews mathematics altogether and instead identifies specific shapes in the chart of stock process (giving them names like "head and shoulders," "cup and handle," "raising pennant," etc.) as a method of predicting that a given security will follow a known pattern given the shape of its current chart
In a word, this is bunkum, but it's very popular among the day-traders these days. In many cases, the patterns can be observed only in arrears, and the patterns are so extensive that you can "predict" anything you want by fitting a pattern of future performance to its current situation.