Natural Harmonics (suggested you are a righty): Take left hand and barely touch the string with your finger(s). Pick as normal and you should get a kind of "twangy" sound. Try this on the 3rd, 5th, and 12th frets for best results. (Example: Verse of "Ravenous" by Arch Enemy")

Pinch Harmonics (suggested you are a righty): These are more difficult than Natural Harmonics and will take time to learn. Push down on any note on the fret board with your left hand. Now, pick the string with your pick and a small piece of your thumb, which will again make a "twangy" sound. If you use too much thumb, the harmonic won't work. Once you get good with Pinch Harmonics, add a little Vibrato to it to get that sound used in common metal songs. (Example: Verse of "Thoughts Without Words" by Shadows Fall)

If there are any more questions, e-mail me.