Bollinger Bands, invented by a guy name John Bollinger, are one of the most popular tools available to traders (both long and short term). Their design is intended to show a relative definition of high and low, via upper and lower bands. The middle band (though not always shown) is a moving average which shows the direction of the current trend.
The working parts
The distance between the upper and lower bands show price volatility. The farther apart they are the more volatile price action is, and the opposite is true when they are close to each other. Most charting software defaults to plotting Bollinger bands with a 20 period moving average, and a 2 standard deviation. However you can adjust this setting to fit your trading style/preference.
Though they can use other forms of moving averages (MA) the most common is the simple moving average. The first step is calculating the simple moving average:
The next is to calculate for the upper band:
Lastly we calculate for the lower band:
Ways of trading
There are many ways of interpreting Bollinger Bands...
1.) Some traders will buy when price is oversold (touching the lower band), and exit when price touches the middle band. The opposite is true for shorts (short when price touches the upper band, exit when it touches the middle band).
2.) Others will wait until price actually crosses above the upper band to long, and to short they will wait until price crosses below the lower band.
Just like most indicators, Bollinger Bands are often used in conjunction with other indicators. Usually the other indicator(s) will be a chart pattern, trendline, or other form of non-oscillating indicator(s).
They are also not just for any one trading instrument, they can be used to trade may things from currencies to stocks to bonds.
My personal take
My personal take on them would be to use the first mentioned way for trading during consolidation (there is no trend, price is in a range). I would use the second way for breakouts from ranges with a trading stop.