Staircase my way down, and then branch/spelunk. Once I find a open cavern, I explore it till I exhaust it, and then dig more branches till I find another cavern. It's pretty random, but I like it. ^-^
I pit-mine. I need literally tons of cobble for my castle, so I basically dig out a huge pit and go straight down to bedrock. Current pit is roughly 15x30, I think, give or take a few blocks. 20x40, perhaps. Big, anyway. No opening to sky above, so it's like a huge cave. Making different farm systems in this cave is also an option, like my tree farm, for instance.
How do YOU Mine?