You would take a train from either airport to St. Niklaus. The trip usually requires one change in Visp and it's slightly quicker from Zürich. From St. Niklaus there's a bus up to Grächen. All details are in the timetable. I would prefer Zürich airport if it doesn't make a difference for the flight.
A Swiss Transfer Ticket is cheaper than a regular return ticket. But if you do more traveling there are other options as well.