Mark the edges of the planned flower box using stakes and strings, a garden hose, sprinkled sand or some other material.
Dig a trench along the planned border. The trench should be about 2 inches wider than the slate wall will be, and the depth should be about half the thickness of the slate plus 2 inches, or a total of about 4 inches. Make the bottom of the trench roughly level.
Add about 2 inches of gravel to the trench. Use a tamper to compact the gravel and make sure that the gravel is roughly level, rearranging the gravel as needed.
Add about 1 inch of sand to the top of the gravel. Smooth the sand out and use the level to make sure that the sand will provide a completely even base for the stone.
Lay the first layer, or course, of slate. Use the heaviest, largest stones for this bottom layer. Make sure that the stones are butted up against each other as tightly as possible.
Set the second and any following rows of slate stones on top of this first layer. Make sure that the stones are staggered so that the joints of one row do not line up with the row beneath it. Fit the stones together tightly.
Fill the flower box in with well-drained, light soil rich in organic matter and plant vegetation as desired.