Step 0: locate a lime quarry.
The edge of a lime quarry will - schematically - look like the figure: lime and a normal dirt floor on roughly equal height.
Step 1: dig down the lime square right next to the dirt as far down as you can. The lime will now be lower than the dirt, including the corners adjacent to the dirt.
Step 2: dig up some dirt from elsewhere, and ctrl+rightclick the dirt onto the dirt square adjacent to the lime square you just dug on. The shared corners will rise as well, allowing you to dig the lime square once more.
Step 3: dig the lime, and head back to step 1
