1st thing you need to do is crank the distortion up to the max and get a nice tone that is neither too bassy or middy.
As the guys above said, hold the pick with about 1 to 2 mm protruding. As you pick the note your thumb should roll away from the plecturm exposing another mm or so, then just as the plectrum passes over the string, your thumb returns to its original position and brushes over the string (creating the harmonic effect).
It helps to sustain the scream sound by adding vibrato. You also get a completely different type of scream depending on where your pick the note (distance from the neck to the bridge).
An exercise to help nail it would be to concentrate on each string at a time and try screaming each fret with 5 different picking positions (eg 1 cm from trem, 3 inches, 5 inches etc). You will very quickly work out the easiest position for you and then it's just a matter of getting the "penny to drop " on the technique for the rest of the fretboard. Like everyhting else on the guitar, its tough to grasp when starting but very easy once you get the idea. Best of luck!