Pry the lip of the slate piece up very gently with the claw end of a claw hammer.
Slide a tool called a "nail ripper" underneath the slate piece while lifting up on the piece with the claw hammer. The ripper is used to either remove or cut the nails which secure the slate piece into place. Most slate pieces are held in place with two nails, although large pieces use four nails. The ripper has a curved end, which must be hooked onto each nail individually.
Move the nail ripper towards the back of the slate piece, then slide the ripper towards the side of the slate piece until the ripper stops at a nail. Pull the ripper downward to hook the tip of the tool around the nail.
Cut through each nail which holds the slate piece in place by striking the flat base of the nail ripper's shank away from the slate with a hammer or rubber mallet. The nails used to secure slate in place, particularly with old structures, are almost always made of copper rather than steel. This softer metal makes cutting through the nail much easier. Sometimes the ripper will actually remove the entire nail rather than cutting through it.
Gently pull the slate piece away from the roof.
Remove any remaining nails from the roof with the claw hammer.