Determine which side of the tile is the face-side. You can tell by looking at which side has the beveled edges. Place the the tile into the slate cutter face-side down.
Position the tile under the blade on the angle you want to cut it. Hold the tile in place with your weaker hand and apply pressure on the blade with the other.
Nibble rather than slice through the slate with the blade. Use short strokes that grind off the slate. Slowly slide the uncut tile under the blade as you cut the line.