This a well covered question already but the technique I personally use isn't listed so I figure I'll add it to the mix. It isn't the technique for strip mining a chunk and extracting absolutely everything but it does expose lots of extra unseen blocks.
It is much faster for quickly gaining things you want, it's incredibly easy to do, and is also less wearing on your pickaxes.
Getting down to and up from the mine:
Use water held up by a sign at the bottom of a 1x1 shaft that is straight down starting up at the surface for dropping to diamond ore levels.
To make it, dig a 1x3 section (so you don't mine beneath your feet) leave one side open for the drop shaft, fill the middle with cobble, and place ladders in the other shaft.
The drop can be as great a distance as you want as long as the bottom of it looks like this:
o = Stone
X = Dug out
W = Water
S = A Wood Sign
L = Ladder
o X o L o
o X o L o
o X o L o
o W o L o
o S o L o
X X X L X ( This is the mine )
X X X L X
The drop is quick and completely safe. I use ladders for the return trip up but, if you prefer, (I think they take too long to make and are unreliable) you can make boat-waterfall ladder for coming back up.
1: Dig the standard 2x1 tunnels away from your entry point. I personally do this standing at Y: 9 so I occasionally run into unexplored caves but, if you are scared of cave mining, do it at Y:8 or Y:7. I don't suggest going to a lower depth than this because bedrock can get in the way, and ore veins that are beneath your feet will be smaller.
2: Every 4th block into your tunnel dig the upper blocks in a 1x1 shaft as far as you can reach on both sides of your tunnel. If you see an ore you like, dig the bottom out and go get it!
The view of walls of your 2x1 tunnel would look like this
x = dug out
o = stone
o o o x o o o x o o o x o o o x o o o x o o o x o o
o o o o o o o o o o o o o o o o o o o o o o o o o o
Extra optional step:
3: If you want to squeeze more out of this type of mine, return once you have finished a good section and bring pieces of TnT. Place them in the back of the 1x1 shafts in the sides of your mine and set them off with Flint n Steel. I don't always do this because making TnT is a pain... but it does work.
General Mining Tips:
1: When mining always place torches on the right wall. When you want to come back just turn around and follow the torches that are now on your left. This is a very helpful technique for not getting lost in any mine exploring or digging.
2: If you have a well enchanted diamond shovel, dig out the sections of dirt you come across. High level shovels obliterate dirt at an insane speed and this typically reveals interesting stuff.
Hope this helps!