The same people who did the mathematical analysis showed slightly lower in this thread that:
▒█▒__▒__ █ blocks you should mine
▒█▒__▒__ ▒ blocks you can see
_▒__▒█▒_ _ blocks you can't see if you don't mine ▒ blocks
_▒__▒█▒_ Repeat this pattern as many times as needed
is more efficient, by about double, than what Strix Suggests.
If your high density branch mine gets you 100% diamonds, the low density branch mine would give you 212.6% ores in the same time, minus 3% from the earlier probability worked out before.
But I use this in single player:
▒█▒_▒_ █ blocks you should mine
▒█▒_▒_ ▒ blocks you can see
_▒_▒█▒ _ blocks you can't see if you don't mine ▓ blocks
_▒_▒█▒ Repeat this pattern as many times as needed
As it is a little more dense, and ore deposits are smaller in single player.
To use the pattern, dig a hall 1x2 across the middle of the diagram, so that it crosses both the upper and lower branch tunnels. Then dig down or up one each time.
Also, you ought to build it so that the floor of the lowest tunnel is on level 11, to avoid falling in lava. If you find that there are few cave systems near your mine, feel free to dig lower, but caves tend to cluster, and caves level 10 and below are filled with lava.
Also, I dig my main tunnel on both sides of the area I want to cover, then dig back and forth in a zigzag patten, which means I'm always digging, never walking.
As for transit? I use a long two wide straight staircase that goes all the way to bedrock. Minecarts work well for getting me deep into the mine.