Minecraft wiki entry for Time-saving_tips, associated text: Mining in caves is more interesting, but also more dangerous. The safest (and, unfortunately, dullest) way to mine is to dig steps down to level 11 above bedrock, and then dig widely spaced corridors two blocks high and one block wide. This is a form of shaft mining; it might reasonably be termed 'corridor mining'. Whenever you encounter any caves on the way, block them off and ignore them. Each corridor should be about ten meters horizontally from any other. Yes, you will sometimes miss small deposits of ores by this method. But the Minecraft world is effectively unlimited, and the object of efficient mining is to hit as many different seams of ore as possible once and once only. Digging twice to the same ore body isn't good, because it wastes effort re-finding a resource you had already discovered. An entirely artificial mining environment like this is safe because it's entirely under your control; there is no risk of mobs spawning in a hidden hole you hadn't discovered, and you can place lights at controllable intervals. Dangerous slimes cannot spawn, and because the mine layout is artificial, it's also very simple, thus making it harder to get lost. The main danger is lava intrusions, but lava now makes bubbling noises when it is nearby, so you should be forewarned. Once you are fully-equipped with diamond armor and weapons, you can then add some variety to your game by exploring the natural caverns.
Variant: using a standalone map editor, you can replace all the stone in a tunnel shaped area with air. This can be used to create a tunnel which is 1 wide by 3 tall by however long you want. Any ores in the carved area will remain since you only told it to remove the stone. Alternately you can first tell it to convert all lava, water, gravel and sand to air, only changing the stone to air after those other annoyances are out of the way. Use this at Y 10 (the tunnel will be heights 10-12) for best diamond-finding results. If you create a series of tunnels spaced 3 blocks apart then any ore that isn't blocking a tunnel will be visible in the sidewall of one of the tunnels.