Boring under obstacles can be done with a high-pressure hose, or you can rent a boring rod that attaches to a vibratory plow. This makes the job much easier. Start by digging about a 4' trench on either side of the obstacle.
Hook up the boring rod (Image 1) and lay it down flat on either side of the obstacle. Bore under the sidewalk at a depth of about 8". Replace a section of main pipe with the control wire (Image 2) and tape both together using duct tape (Image 3). This will ensure that both wire and pipe can be snaked under the obstacle. By taping the end of the pipe, it also prevents any debris from getting into the pipe.
Start by gently removing the sod with a landscaping shovel (Image 1). Place all of the sod on one side of the trench (Image 2). Dig out the trench to a depth of about 8". Place the dirt on the opposite side of the trench. Using a trenching or clean-out shovel, remove all of the dirt so there is a flat bed on the bottom of the trench. Cut the poly pipe to length and place down flat on the bottom of the trench bed. Using a clean-out shovel, backfill the trench and replace the sod (Image 3).