A lot of it is common sense, but it's mostly "go fast, and go big." Get as many quests as you can, and do them all at once. Pop all your cooldowns whenever they come up, and even while you're looting something, be looking for the next quest target or the next thing to kill. Professions are out the window, of course, and reading quest text will just slow you down, so just click accept, and read what you're supposed to find while you're running out to find it.
In case you're wondering, no, I don't recommend playing the game like this (it's fine to be a slow leveler), and even Matt admits that you'll miss out on pretty much everything pre-80, including all of the lore and story Blizzard's baked into the game this time around. But if getting to 80 is your only goal, his tips will help.