Tune your guitar down a half step. Van Halen's guitar is tuned to Eb on the recording. Relax the tension of the low E string so that the sixth fret is the equivalent of the open A string. Then relax the A string by the same amount so that its pitch is the equivalent of the fifth fret of the string. Repeat this process with all strings so that each is a semitone lower than normal. When tuning the B string, use the fourth fret on the G string as the tuning reference.
Plug a 1/4-inch instrument cable into the input jack of a phaser pedal. Connect a 1/4-inch jack patch lead to the output jack and into a delay or echo pedal. Connect a second patch lead to the output of the delay and into an overdrive pedal. Van Halen used a phaser, echo and overdrive pedal to achieve the distinctive tone on "Eruption." You can emulate the tone using your own pedals. Turn all pedals on and tweak the parameters until you have a warm, slightly out of phase tone.
Place your right palm gently against the strings, just above where they are attached to the bridge. This is called a palm-mute. The distinctive "muffled" sound Van Halen teases from his guitar toward the end of the first section is achieved with this technique. If the strings are ringing out while you play, use a little more force with your palm.
Depress the tremolo arm fully down. Whenever you hear a rapidly descending note, Van Halen achieved this with the tremolo arm. It's tempting to emulate this sound with a downward slide, but for authenticity it is imperative that you use the tremolo arm.
Tap the string against the fretboard. This solo is famous for the two-handed tapping section, as it was one of the first prominent examples of the technique. To achieve the rapid and fluid note changes, place the first finger of your left hand on fret 12 of the top E. "Hammer" your left hand third finger onto fret 14 to create a two-note sound. Then "tap" fret 16 of the same string to create the distinctive triplet pattern that Van Halen made famous.