Basically, Metal is a subgenre of Rock and is loosely defined by the instruments used.
It's not easy to pinpoint the exact subgenres as Metal bands often combine various styles from in- and outside of Metal.
Often new genres emerge through a location or as a movement in a country and sometimes slowly begin to disappear after a while. Gothenburg Death, German Power Metal, Bay Area Thrash, Florida Death, Norwegian Black Metal; you name it.
I don't think there is any point in time that can be described as a Big Bang of Metal. Some argue that bands like Deep Purple, Uriah Heep, Wishbone Ash or Blue Öyster Cult were the first Metal bands and that is true, to some extent, as they share a lot of motifs like epic lyrics, featuring fantasy stories and often based on literature. But by modern standards, they really are just Hard Rock. The most influential band in this context would be, of course, Black Sabbath.
The best way to begin would be the New Wave of British Heavy Metal that brought us bands like Iron Maiden, Diamond Head, Motörhead, Saxon and a lot of other, lesser known bands. From there on, some bands decided to play Metal a bit faster and it was called Speed Metal. Then it also occurred that the band Venom released the album "Black Metal" and while it wasn't very good, it was highly influential to not only Black (duh) but also Thrash Metal.
Sometime in the mid-80s, the Swiss band Celtic Frost released the two albums To Mega Therion and Into The Pandemonium which remain to this day two of the most influential records in Metal history, especially for Extreme Metal.
Now Extreme Metal doesn't mean anything at all, it's just an umbrella term for Thrash Metal, Doom Metal, Death Metal and Black Metal. Contrary to popular opinion, Grindcore is not Metal. As the -core suffix suggests, it's a subgenre of Hardcore Punk These are not called Extreme Metal for nothing, though. Not only do they (mostly) sound extreme but also contain extreme lyrics - despair, suicide, violence and similar things. They also have very... unique scenes.
All of that branched out in the 90s and nowadays we have so many (useless) subgenres that I can legitimately say that I can show you anything, from "Scottish Pirate Metal" to "Electronic Art Metal" from Greece.