Put on your safety gear. Place your tile on a cutting surface. Hold it in place with your foot or free hand, or clamp it down with a clamp.
Place the center of your core bit into the center of your marked-out area. Press the trigger gently while applying downward pressure to sink the pilot bit into the face of the tile.
Wait for the pilot bit to dig into the face of the quarry tile. Once it is set, pull the trigger completely and push the core bit through the quarry tile until it is through. Remove the cutout to reveal your circle cut.
Wear your safety gear. Turn on the wet saw. Hold the tile firmly in both hands while resting it on the tray. Push it into the saw until the blade reaches the edge of your marked crescent.
Repeat the process every 1/8 to 1/4 inch across the width of the crescent, giving a “jail bars” look to the tile. Knock the slivers of tile out of the crescent, revealing the “broken teeth” of the remains along the edge of the crescent.
Smooth the “broken teeth” section with the blade of the tile wet saw. Guide the tile blade along the crescent mark while slowly moving the tile with your hands, easing away/cutting away the remains until you have a smooth reveal.
Put on your safety gear. Place your tile on the cutting surface. Set the tip of the angle grinder blade against your circle cutout mark. Turn on the machine and apply gentle pressure as you allow the grinder blade to slowly sink into the surface of the tile around the entire perimeter of the circle.
Make slow, even passes around the edge of the circle, cutting down around one-third of the way through the tile. Then, make two cross-wise cuts (a cross hair) across the circle, cutting down all the way through the tile with the grinder blade to create four quarters within the circle. Apply slow, gentle pressure and cut slowly to avoid breaking the tile.
Go back to the perimeter of the circle and dip the tip of the grinder blade in once again. Apply gentle pressure and slow, even passes, going back and forth over the line until your blade finally breaks through the face of the tile. Repeat the process with each quarter of the circle.