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Tapping adds a whole new dimension to your guitar playing and in a way resembles piano / keyboard style since you are striking down on the notes with both hands rather than just one hand and picking with the other.
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The traditional way is to use the index finger of the right hand (reverse for lefties) to tap down on the high notes and usually have two notes in the left hand that your hammer on and pull off. Your first finger on the left hand is holding down the C on the G string as in the example below.
The first example is the traditional triplet (or sextuplet) tapping pattern in the style of Eddie Van Halen. Notice how easy it is to form a chord between the three notes and then change chords. The chords below go from a C to C # 5 to C6 to Cdom7 by changing one note at a time in the right hand.