Mark the location of the trench by spray-painting two lines onto the pavement that are about 1 foot apart. Place the slot drain in a location where water usually collects, such as at the bottom of a slope.
Put on safety goggles, ear protection and gloves.
Place the tip of the jackhammer on one of the spray-painted lines, and lean the top of the jackhammer slightly toward you. Hold it firmly, and begin digging a hole in the pavement, working the tip of the jackhammer inward. Stop when you reach about halfway between the two lines. Tear up the pavement on the first side of the trench, using this process.
Remove the pavement for the other side of the trench, starting at the other spray-painted line and working in toward the center of the trench.
Clear the debris out of the trench.
Straighten the trench walls as much as possible with a hammer and chisel. Dig out the soil in the bottom of the trench -- so that it's deep enough to hold the plastic drain channel and a 2-inch-deep sand base. Level the soil in the trench.
Pour the layer of sand into the bottom of the trench and smooth it, sloping it down toward the area where you want to drain the water, at a rate of 1 inch for every 20 feet of run (length). Do not slope the drain toward your house, as it can cause flooding problems.
Assemble the drain channel, following the instructions provided by the manufacturer. Assembly instructions can vary between manufacturers and models of plastic drain channels.
Apply a bead of silicone adhesive onto the joints between the different sections of drain channel to help seal them. Skip this step if the manufacturer's instructions say not to do it.
Cover the grate on top of the drain with duct tape to prevent concrete from falling into the drain channel.
Place the drain channel into the trench, centering it inside the trench.
Mix a batch of concrete, following the instructions on the packaging.
Pour the concrete into the trench between the trench wall and the side of the drain channel. Fill a section about 2 feet long on one side of the trench, then fill a 2-foot section on the opposite side.
Smooth the surface of the concrete with a trowel, blending the concrete with the surrounding pavement and creating a slight slope down toward the drain channel. If the concrete is higher along the edge of the drain channel than around the surrounding pavement, it will block water from entering the drain.
Fill the rest of the trench with concrete, using the same process. Allow the concrete to cure for four to five days, then pull the tape off the grate.