Where do I find diamonds in Minecraft fast?

Find someone elses diamonds and take them

Diamonds normally spawn around lava and lava doesn't start to spawn until about level 16 but diamond can be found better in lower levels such as 6

Dig down to level 12, which keeps you just above lava level. Dig horizontally and eventually you'll hit lava pools that you can dig around. They have a pretty good chance to have diamond deposits.