Well, for practical tips, it would really help to know what SORT of screaming you want to do. You mentioned hardcore, and that's basically just shouting, unless you're referring to something different. The type of screaming basically depends on where you vocalise, if that makes sense. Classic death metal screams come from the back of the throat, up top. Black metal vocals come from way deeper down in the throat, and employ less technical aspects: you really just scream until you start coughing up blood, then you drink some more. Or at least, you do if you want to avoid the cookie monster. Piq squeals come from practically up in the nasal cavity. The real trick is simply to practice. Most people, if they did a proper death metal growl, would probably start coughing or maybe even throw up*. A lot of people never do proper growls, and there's lots of ways of faking up the sound (for example, putting massive overdrive onto whispers can sound a lot like the real thing. I'm reasonably sure that's what Brendon Small uses to do Nathan Explosions singing voice in Metalocalypse).
*I've seen this happen.