Switzerland's rail network, SBB, has one of the clearest and most generous pet policies in Europe. A dog under 30cm tall at the shoulder travels completely free as hand luggage, as long as it's in a suitable closed carrier, basket or bag placed under the seat, not on it.
Larger dogs need their own ticket. The simplest option for visitors is the Day Pass Dog at CHF 25, which covers unlimited travel for one dog for a full calendar day across SBB trains, most lake boats, PostBus routes, and trams and buses in most Swiss cities. Frequent travellers can also buy a Monthly Dog Pass (CHF 60) or Yearly Dog Pass (CHF 350), both tied to the accompanying person's SwissPass.
Larger dogs must stay on a leash, muzzled, and positioned so they don't block the aisle. They're not permitted in dining cars or on the Glacier Express, since food is served throughout that route — plan a different train if travelling with a dog that size on that specific line.