Hello Rkymtnbamagirl
In order to book group tickets online, which isn’t that trivial, please create an SBB account first on www.sbb.ch
When done so, make sure you are logged-in so you can book the ticket online; simply fill in the form and enter the start / end destination in the timetable query form.
Yes, the train stations you need are ‘Zürich Flughafen’, and ‘Zermatt’.
Online booking is possible provided the trains / buses etc. you would like to book offer a sufficient seat capacity. If not, or in case a connection is not available for online booking at all, you have to call SBB: +41 51 225 78 56 (24/7, waiting times may occur).
Some people do not bother with the online booking at all and simply call SBB to make the booking. In doing so, they have an instant response whether the planned trip is feasible or not; moreover, they can clarify in person their questions they might have with a friendly and helpful SBB agent
Kind regards,
Roland