Listen to some deathcore or metal bands that feature screaming in their music. Pay attention to the tone and character they evoke with the screams. Finding a style that suits you is a good way to find your own voice as a singer.
Breathe properly to prepare the voice. Take a big breath of air through the diaphragm by expanding the stomach and the chest. Avoid tensing up the shoulders and the neck. Release the breath slowly and silently. Keep your back straight and chin slightly downward.
Warm up the vocal chords by taking a deep breath and releasing it through the larynx, letting your chords resonate on a note. Don't be concerned about any pitch, just let the voice find a comfortable note. On the same breath, move the pitch upward to the top of your range while keeping shoulders relaxed. Move the pitch downward to the bottom of the range.
Take another deep breath, this time singing the lowest note possible. This should sound more like a croak than a note. Singing in this manner is known as the vocal fry. Move up in pitch while retaining the vocal fry timbre.
Push harder from your abdomen to force more air into the vocal chords. At this point the sound should be far more breathy than tone or note oriented. If you are feeling strain in your voice, produce more breath and less sound. Keep the breath stream moderated.
Try resonating the sound in the bottom part of your neck for a low scream. For a higher scream aim more for the nasal cavity. Always push the breath from the diaphragm.