How do I find out where to pick up my checked luggage?

There are various general rules of thumb, as described by Jim in his answer. But to answer your specific question:

How do I find out, would I need to call Swiss air to find out?

In case of any doubt, ask the airline agent when you hand in your luggage. They'll know exactly how they tagged it, and are also the ones to know about cases where you may need to pick up your luggage even though it is tagged to a later destination (such as for an international-to-domestic transfer at a US airport).

If you need to clear up your doubt before flying (such as if you have a transfer in a country that you can't enter without a visa), calling the airline to make sure would indeed be the recommended procedure.

Specifically for Zurich (or other European hub airports), if your layover is not overnight and both legs are on a single booking with the same airline, you can be virtually certain that you will not need to pick up checked baggage during the transfer.

Assuming all legs are on a single ticket, you will certainly pick up your bags at the last airport. Often (if not usually), when you clear Customs and Immigration at an airport in the middle of the trip, you'll claim your bags there, too, to clear Customs (although there are increasing exceptions, such as at many airports in Canada).

Also, if you have an overnight connection, you can often have your bags checked to be picked up at your connecting airport, so that you can have access to your toiletries and clothes.

Otherwise, you can request what's called short checking - your bags being available at a connecting airport, even though they usually wouldn't be - although the airline may not be willing to do this. They may not allow this, to prevent what is called hidden city ticketing, where people abandon flights early to get lower fares compared to booking to the airport they really wanted.