Place the painters tape in the shape of an "X" on the slate tile where you want to open up the hole.
Mark the tape with the marker on the spot you want to make the hole.
Place the carbide-tipped masonry drill bit onto the drill. Get the drill bit straight before locking it in place or it can damage the slate finish.
Place the drill on the slowest speed setting possible.
Start slowly drilling on the mark placed on the tape until you pass the top layer of the slate tile. Change to a faster setting and continue until you open the hole completely through the tile.
Remove the tape and blow off any dust. You can now insert a wall anchor or other device into the slate tile.