Warm up the vocal cords. It is easy to over-stress, pull, or even tear vocal muscles that are cold. Try some vocal scales beginning in your natural range and extend the notes up and down from there. Sing "ga" on all notes to start. Lastly, sing through with "ay," "ee," "ah," "o" and "oo".
Scream like you sing. Scream into the "facial mask" by opening the very back of your throat and directing the sound from your diaphragm through the open back of the throat and out of the body through the nose. Singing through the nose is essential in preserving the voice for anyone who sings, screams or even talks for long periods of time. Close your mouth and hum on one note for as many beats as possible. Feel your nose vibrate due to the sound coming through it. That is the proper placement. Continue humming while you slowly open your mouth. Screaming while keeping the sound placed in this manner within the throat and nose significantly reduces the stress on your vocal cords.
Support your scream from your diaphragm. Breathe low into your stomach and use your diaphragm muscle as a floor for that breath. Keep the muscle firm as you sing to support the sound in your throat with a cushion of air. This cushion keeps you from grating your vocal cords together.
Shape the beginning of your scream into a "ya" or "ga" sound rather than a straight, open-throated "ah." This makes the initial blast of air through the vocal cords much less stressful on the cords and throat.
Keep the back of your throat open throughout your entire scream, but do not push more air through your throat than is necessary. Practice singing or screaming in front of a lit candle and try to keep the flame from flickering.
Put all the requirements together and produce a less-than-full scream. Don't give it all you've got in the beginning. Give yourself time to learn to do it correctly before you put real power behind your scream.
Plan your screams and their individual strengths in advance of a performance. Know in advance when to pull out a full-powered scream and when to scream with less oomph.
Warm down with an abbreviated version of your warm up. This allows the muscles in the throat to slowly return to their normal state.
Talk as little as possible after a performance and try to avoid making any loud noises to give the throat a chance to rest.