Zurich to Interlaken

There is a train station at the airport and some trains go to Bern, where you can connect to Interlaken. Check precise times and connections at https://www.sbb.ch/en/home.html

Yes there is a station at the airport. There are several routings. Some have a train change at Munich Hbf and Bern, and some go direct to Bern where you change trains to Interlaken. Since there are several departures every hour, you can choose to wait for one with only one change.
Check at www.sbb.ch/en
The ones at 40 past the hour have a single connection in Bern with and easy cross platform transfer from Track 5 to Track 4.

Choose a route that goes through Luzern. The ride from Luzern to Interlaken has some of the best natural scenery for a route that does not have a theme.

That's an option. It is shorter as the crow flies, but takes a little longer and requires changes at Zurich Hbf and Luzern. Yes, much more scenic. Might also be a franc or two cheaper if you are not using a pass.

When are you making that trip? I ask because normally you can catch the train at 47 minutes after each hour from Platform 3 of the Zürich airport (Flughafen) and take it directly (without changing trains on the way) to Luzern. Then you change to the train on Platform 12 in Luzern that leaves at :06 minutes after each hour to take the very scenic ride directly to Interlaken Ost. That's the most scenic way.

However, when I looked it up on the web site (www.sbb.ch/en) for April, it shows that passengers have to change to a bus on the way, and then back to a train. So then I looked it up for July, and it was showing the normal all-train route.
I assume there's some construction going on, presently.

The station at the airport is called "Zürich Flughafen". If you enter "Zurich airport" in the SBB website ( https://www.sbb.ch/en ), it will display as Zürich Flughafen.
You will need to change at Bern. This will be easy, in many cases opposite sides of the same platform.

There are two stations in Interlaken, Interlaken West and Ost. Coming from Bern you will stop at West first, then Ost which is the end of the line and the interchange point if you are going beyond Interlaken.

The alternative slower but more scenic route is via Luzern. This ends at Interlaken Ost (no West)

Sam,

"Some have a train change at Munich Hbf and Bern, and some go direct to Bern where you change trains to Interlaken."

I assume you meant Zürich Hbf in your first reply and not Munich?

Here's another question - does anyone know what time the gondola's start running? We hope to leave Gimmelwald at 6:30am - is that possible?

The same train schedule links will also reflect the lifts to/from Gimmelwald, Muerren, etc.

Using the www.sbb.ch/en website, I see that the first cable car down from Gimmelwald starts at 6:00. They're every half hour after that.

Print this itinerary and carry it with you. It will get you anywhere you need to go in the Lauterbrunnen valley: https://schilthorn.ch/cmsfiles/fahrplan_2018_web.pdf