How do I identify second class carriages in Switzerland?

You can minimize the number of changes (down to 2) by choosing the right train at the airport. Some trains go from there to either Bern or Luzern without a change at the main station. They do stop there, but you do not have to change trains.

How do I know to stay on the train? So far, I have seen that arrivals and departures are on different platform so I guess if I see an arrival and departure on the same platform within 5 minutes, it's the same train?

You should know when you board the train at the airport that it is one that goes to Bern (or Luzern) without a change at the main station. You can use the Swiss rail site (rail.ch for English) to figure it out. For example, going the Bern route to Lauterbrunnen, you'll see a departure from the airport at 9:40 with 2 changes on the way. Click on the little plus sign to the left and it will show the changes, at Bern and Interlaken Ost. Click on "show intermediate stops" and you'll see that the train stops at Zurich main station, but continues on to Bern. You stay on the train. Compare to the train that leaves at 9:43 with 3 changes. Click for details and you'll see that you change trains at the Zurich main station---you come in on IC 518 and arrive at Track 14, and you go to Track 16 to board the IC 818 for Bern. (This is the same train you could have caught at the airport at 9:40).

Look for the Giant "2" on the outside of the carriages to find the second class ones. That will tell you which are first/second class cars.

Perfect. That was easy.

Got it! Thank you for the tip. The less changes the better. I am printing the schedules with all the stops to be sure.

Excellent. I like to include several options, with departure times extending over an hour or so, just in case our plane arrives later than we expected (it never has.) Have a great time in Switzerland. I wish I were there right now. Even the airport is fun (the little train between terminals has Swiss sounds to welcome you.)

"if I see an arrival and departure on the same platform within 5 minutes, it's the same train?". Not necessarily. Particularly in small stations, I've seen a train come in on a track, let people off, and leave, with the connecting train coming in a few minutes later, on the same track. Look at the schedule. Each pair of lines of lines are the start and end of a train's run. If the destination on one pair is the same as the start on the next pair, even if they have the same track number, it's a connection. Check the train numbers; they will be different. Generally, you won't see a station listed on the schedule unless it's a connection.