Rent a wet saw from your local home improvement or tool rental store. Ensure you have the correct blades to cut concrete. Wet saws aren't cheap, so if you're unlikely to need one again anytime soon, there's little point in buying one. It's possible to rent or buy walk-behind and handheld wet saws. A walk-behind model will be safer than a handheld saw, but offers less maneuverability.
Prepare your wet saw for use as per the manufacturer's instructions. The method for doing so will depend on the make and model of saw you're using.
Put on your safety goggles, mask, gloves and a pair of steel-capped boots.
Connect your saw to a water and a power supply. Some wet saws, particularly walk-behind models, run on a gasoline/oil combination.
Check to see that there are no people or animals in the near vicinity before you start. Shards of concrete can be projected from your saw while you cut.
Start your saw away from the ground. Then, remove sections of concrete in squares or rectangles. Cut the bottom horizontal line of your square or rectangle first, then two vertical lines, followed by the top vertical line.
Remove the section of concrete you've cut with a crowbar.
Repeat the process to remove the rest of your concrete.