Adirondack Mountain News posted a very good summary of what happens in New York whenever a hiker needs help from the rangers.  This is specifically the process that is done in NY where we're relatively unique in that the Rangers are in charge of all SAR activities on state lands.  Other locations in the country it could be any number of agencies and isn't always consistent with who is in charge.  That said though, the overall process and the insights into how the searches are run should be consistent across the country, if not world.  The full post by them is here: