customs at airports in Germany and Switzerland

Customs, immigration, and security are three different things. Americans often use the word "customs" to refer to all of them, but the difference does matter.

In Europe, it's immigration (passport control) that can take time. Customs is just a matter of walking through the "Green Channel - Nothing To Declare" line. It's rare to be "randomly selected for additional screening," but this is possible (I saw it once in Poland); unless this happens to you, you just keep walking and exit the airport.

If you are all on one ticket, you will go through immigration in Frankfurt (your first entry into the Schengen zone). You will go through customs in Berlin (your final destination on the ticket). You may or may not go through security for your plane changes, depending on exactly which terminals are involved.

If you are on separate tickets, you will go through immigration and customs in Frankfurt (again, immigration can take time, customs does not). Flights from Frankfurt to Zurich and Zurich to Berlin are all within the Schengen zone, so there are no further routine immigration checks. You will use your passport for ID, but it will not be stamped or looked at by border agents. Switzerland is not part of the EU, so technically there is customs between them and EU countries, but again, this is a walk through unless you have special circumstances (something to declare) or are stopped for extra screening. You will likely have to go through security if you're on separate tickets, but again, this depends on the layout of the airport and the exact airlines involved.

If it helps: As somebody who frequently flies between FRA, ZRH and BER there is nothing to add to Harold's respone.

Sometimes, though not always, upon boarding an intra-Schengen flight they want to see your picture-ID along with your boarding pass upon boarding the aircraft. In such a case use your passport, not your driver's license (even though Europeans will only show their ID cards).

Andreas: thanks for the validation!

Yes, Andreas clarified what I meant about passports. If you are asked for an ID at the airport, you use your passport (your US driver's license would not be accepted as ID in Europe). But that's different from immigration, which (in this scenario) normally only takes place when entering or leaving the Schengen zone.

Thank you, Harold and all the others who gave such thorough responses to my question about immigration in the Frankfurt, Zurich, and Berlin airports. It's great to have this travel forum available!!