Getting on a train at the Zurich airport

It's easy, go the the train station inside the airport and buy your ticket(s).

https://www.flughafen-zuerich.ch/en/passengers/shopping-and-enjoy/services/all-services/sbb-reisezentrum

Scroll down to where it talks about where to purchase SBB tickets.

Follow the train icons after you get your luggage and exit customs (walk out the "Nothing to declare" door).

You can purchase tickets either from the machines or from the agent at the window. Last time we used the machines, they required a PIN for the credit card, which we had on our debit card so that worked. I don’t know if that is still the case.

Just be sure you buy tickets before boarding the train. You cannot cut them on board, and there is a serious fine if they happen to be checking tickets.

Look into a train pass if you will be staying in Switzerland for a few days. With a pass, you just get on the train, no need to buy individual tickets.

You can also buy tickets on your phone using the SBB and ZVV apps. SBB is the national rail and ZVV is the canton of Zurich's local public transit system, although you can buy tickets for at least some trips outside of the canton on the ZVV app as well.

The apps generate a QR code for your ticket that will be scanned by SBB/ZVV personnel if they approach you during your trip. Unlike in other places, you do not scan the QR code yourself to enter public transit (i.e., through a turnstile), you simply board and take a seat. Your tickets may not be checked by anyone, but if you ride without a valid ticket and get caught, you will have to pay a fine.

When you buy tickets on these apps, they will be time-specific.

The only tickets that are times-specific are the super saver tickets. Standard tickets are not time-specific.

The man in seat 61 details the differences between the different types of tickets in Switzerland.

https://www.seat61.com/train-travel-in-switzerland.htm#Saver_Day_Pass

@Reiselle, while this is true, the validity period is the entire calendar day for which the ticket is purchased.

Referring to them as 'time-specific' might cause unnecessary concern for travelers. As Carrie mentioned, this phrasing is more commonly used to explain the difference between super saver tickets and regular point-to-point tickets.

Edited to say: There are various local tickets, like the ones I purchase for the bus, which are only valid for 30 minutes. However, most tourists are not usually interested in these types of tickets.

Regional zone based tickets (like ZVV tickets) are valid only for a couple of hours after the time selected during purchase. And as a tourist you will increasingly encounter these.
One example is Interlaken - Bern, where tickets now are sold according to the Bernese "Libero" tariff, which means that a ticket is only valid for 3 hours. But it is also good on busses and trams in Bern for example within that time. If you buy a return ticket you get a day ticket, valid on all public tansport in the zones that cover Interlaken, Bern, and the route in between.

And the intention is to move the whole country to a zone based system.

Thanks for the clarification. I learned something new!