So you've arrived at your hiking trail and are about to set out. Presuming you have mobile phone reception, first call a responsible party - who already knows where you're hiking - and let them know you have arrived at the trailhead. Remind them again of when you plan to return.
Make sure you stick to this schedule. If you haven't arrived home within an hour after the time you planned and have had no communication with this person since arriving at the trailhead, they should contact authorities (such as the park ranger or local sheriff's office) to report you lost. You also can sign the trail register, if one is available.
Read more about day hiking with children in the guidebook Hikes with Tykes.