First you will need 3 iron picks. Dig a 28x28 area down to level 8. You can see the level by pressing f3 and the y is the level. You have a 40% chance of finding diamonds and a 60% chance if you see a cave or lava pool. This is to do with chunk generation. If you don't find diamonds dig another 16x16 area next to it. The default chunk size is 16x16 if there is a 50x50 area there will be at least 1 vein of diamonds.
-Thanks Bee