After stealing some stuff from BNR:
Thrash is a mixture of NWOBHM, speed metal and extreme hardcore. It uses a fast pace, a staccato, chunky guitar riffing style, and aggressive vocals. Venom were one of the biggest influences on the style although many people think it didn't start till Exodus, Overkill and Metallica. (Joe recommends: Slayer, Kreator, Coroner and Dark Angel).
Death metal grew out of thrash in the late 80's it uses lower tuned riffs, chaotic song structures, deeper growled vocals and usually morbid lyrical themes. Slayer had a major influence on death in the same way Venom did on thrash but Possessed were arguably the first death metal band. (Joe recommends: Autopsy, Morbid Angel, The Chasm and mid-period Carcass).
Black metal as a genre is defined mainly by ideology since there are few similaritys between bands generaly accepted to be part of the genre. The main points are a hatred of western culture and morals as well as a strong loathing of the Judaic religions. This is usually represented though Satanism, Paganism, National Socialism, Nhillism or blasphemy against organised religion. But more than this black metal proposes an alternative in the rejection of ethical values and the reliance on will power of individuals. Venom released the first black metal album at the start of the 80s with "Welcom to Hell" and since then the music has spun off in a hundered different directions with scenes who practice their own distinctive sounds appearing all over the world. (Joe recommends: Burzum, Necromantia, Bathory and Grand Belial's Key).
It should be noted that while I belive most of this stuff to be correct there will always be arguments over details (and in the case of BM they're big details) so this shouldn't be taken as gospel.