Place the countertop right side up on sawhorses or a worktop.
Measure the locations and dimensions of the openings you plan to cut, and mark them on the countertop. For sinks, place the sink upside down on top of the countertop after measuring the sink location. Trace around the sink's outline, then remove the sink and make a second cutting line one-half inch iinside the traced line, using a straightedge. For an L-shaped cut in the countertop, trace a square placed in the corner to ensure a 90-degree angle.
Clamp the countertop to the sawhorses or worktop with C-clamps or vise grips. Clamp a straightedge or a straight piece of wood outside the first cut line to guide the shoe of the circular saw so that the blade cuts straight down the line.
Mask around the cut lines with cloth tape.
Place the saw’s shoe firmly against the straightedge. Lift the guard on the circular saw to expose the blade. Hold the back of the saw's shoe firmly on the granite surface, angle the top end of the shoe upwards and hover the blade directly above the first cut line. Start the saw, and slowly lower the blade down into the line. Move the saw slowly forward to cut along the cut line. The water-feed system on the saw will keep the blade cool.
Re-situate the straightedge outside the next line. Cut the adjacent line in the same manner. Continue until all inside cuts are complete.