Trains from Vienna to Zurich

No difference with any other train. There is no, repeat no procedures to go through before you get on the train. You just need to be on the platform and get on the train before it departs.
Like all long distance trains, it has many stops, Linz, Salzburg, Innsbruck, Feldkirch, Buchs and many others. Only a minority of the travellers go end-to-end, most seats will have two or three different people occupying them along the way, making trips between intermediate stations.

The actual border crossing takes place between Feldkirch and Buchs AG. The train crews change at Buchs. There is no formal passport control as both countries are in the Schengen Area. Customs officers may get on the train and walk through, perhaps asking a question of one or two people per coach. That is all.
Try not to look like an international drug courier or an illegal immigrant, and they will ignore you ☺.

Interesting fact: The train passes through Liechtenstein between Feldkirch and Buchs, but it doesn't stop there (unless it gets a red signal). So you can add one more country to your list.

Awesome. Thanks Chris! I was planning to be there 30 mins before the scheduled departure and looks like that will work.
I will be traveling with kids from California to Vienna and Switzerland. So, trying to avoid anything with long wait times. Train journey seems less expensive than flights but much longer. Hopefully, the kids will enjoy the train ride.
I am also hoping the train station will be easy to navigate thro'.

Arriving 30 minutes before departure sounds about right if you are herding kids. Most stations have food and drink stalls where you can buy supplies for the journey. This will be more choice and cheaper than you can get on the train.
The station is called Wien Hauptbahnhof" (abbreviated Wien HBf). I found this plan by googling: http://wien-hbf.at/hauptbahnhof_wien_plan.html
It is a new station, so it is a simple layout. You can look up your platform number before you get to the station
Older stations that have been extended and re-built many times can be complicated (Zürich HB is on 3 levels, two underground!)

See this webpage for lots of info about the Vienna -Zürich trains: https://www.seat61.com/international-trains/trains-from-Vienna.htm#Vienna-Switzerland

I hope you have been told the usual stuff about Switzerland: don't stay in Zürich, go to Luzern or the Jungfrau region.

It is pretty far by train Vienna to Zurich. I would check and see how much Swiss ,International Airline flights are nonstop. It is a route not well serviced by budget European air carriers.

Interesting fact: The train passes through Liechtenstein between Feldkirch and Buchs, but it doesn't stop there (unless it gets a red signal). So you can add one more country to your list.

Yet another coutry to add: it passes nonstop through Bavaria too (between Salzburg and Kufstein).