Hi Jack,
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.
All you need to know about traveling by train, bus or car in Switzerland.
Hand picked Swiss hotels and other accommodations are right here.