ADX (Average Directional Index)
DMI (Directional Movement Index)
(Revised July 03, 2011)
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In these tutorials I will discuss what to do when you visually look at a technical indicator or oscillator on a chart, I won't discuss math jargon or history, I think it's more important to know how to react at a glance (what is the chart saying), therefore only consider this an introduction in brief based on my opinion.  You should educate yourself further if interested. The charts used are not invitation to buy or sell, and are used only for example purpose.
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Intro
The ADX and the DMI +/- are used together  to find  a trend, it's direction and the trend strength.  
The interpretation of this technical is straight-forward but successful implementation takes practice.
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So how does it work?
This oscillator is made up of 3 lines crossing each other; one called ADX, the others called DMI+ & DMI- with a scale on the side numbered 0-60
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Lets look at the lines separate for now.
The ADX line is to find the strength of the trend or if the stock is even trending to begin with.  
The basics are: if the ADX is above 25 there is a strong trend present. Above 50 the trend could be getting fragile.  If the ADX is below 20 there is no trend present and this market should be avoided. (I would use these numbers as a baseline but fine tune it to your preference)
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The DMI lines are used to find the direction of the trend.  If the DMI- crosses above the DMI+ then it means a bearish trend will prevail.  Likewise, if the DMI+ crosses above the DMI- then a bullish trend will prevail.  You should avoid markets where the DMI+ & DMI- are moving sideways together or close to each other to avoid false signals.  
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Putting it all together
Notice in the chart below there was only one true "buy" and only one true "sell" signal even thought the DMI lines crossed again in March, April and twice in May.
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BUY signal: when the DMI+ crosses above the DMI- while the ADX is above 30
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SELL signal: when the DMI- crosses above the DMI+ while the ADX is above 30
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WARNING!!! reversal may be happening soon: when ADX is above both DMI+ and DMI- lines or above 50
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No need to enter the stock when the ADX is below 20 or below both DMI lines
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So what do I think?
I think the ADX/DMI oscillator can be used easily to locate trends that are going to reverse (the warning sign). However to master the DMI lines for "buy & sell" signals; it will take much practice.  I would suggest you use other technical indicators to compliment the ADX/DMI signal. Having said that, I find it is one of my favorite trend busters, and you may want to read more information on this technical oscillator.
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IMO, not one technical indicator should be used by itself.  The more indicators that line up to confirm the signal the better chances your trade will succeed.
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Good luck on all your trades and or investments
And happy capitalism