Mark the location of the drainage trench onto the concrete with spray paint. Make the lines 4 inches wider than the trench will be.
Dig up the pavement between the lines with a jackhammer. Begin by placing the tip of the jackhammer on one of the lines, and work in toward the center. Tear up about half the trench from one line, then go to the other line and tear up that side. Remove the chunks of concrete as you break them up.
Remove the soil in the trench until it's deep enough to hold a 2-inch layer of sand and the plastic drain channel.
Pour the sand into the trench, sloping it toward the area you want the water to drain to (don't drain it toward the house). Slope the sand 1 inch for every 20 feet.
Construct the drain channel according to the manufacturer's instructions.
Lay the drain channel into the center of the trench.
Cover the grate on the drain channel with tape to protect it while you pour the concrete.
Mix a batch of concrete, following the instructions on the packaging.
Pour the concrete into the gaps between the drain channel and the patio, smoothing it out with a trowel. Allow the concrete to set for at least 4 to 5 days.
Take the tape off of the grate.