Dig a 12-inch trench with a shovel that is aligned perpendicular to the sidewalk at the point where you want the sprinkler line to cross under the sidewalk. Continue the trench on the other side of the sidewalk in the pattern that you want the sprinkler lines to run in.
Turn on your pressure washer, and lay the wand in the trench with the nozzle pointed at the dirt just below the sidewalk.
Pull the trigger on the washer and begin to slowly push the wand under the sidewalk. The water pressure will force the dirt in front of the wand out the back, toward you.
Continue moving the wand forward until you have tunneled under the entire length of the sidewalk. You will feel the sprayer lose resistance once it reaches the other side of the trench.
Remove the wand from the hole.
Lay the sprinkler supply pipe in the trench and feed it through the hold you just created. Finish connecting sprinkler pipe before filling the trench with dirt.