You need to observe a few rules if you wish to keep your pets with you when settling in Switzerland. In brief:

Vaccination
Switzerland is a rabies-free country, and thus cats and dogs no longer have to undergo periodic vaccinations. If, however, you plan on traveling abroad (especially to France), your pet must be vaccinated at least one month prior to your departure.

Permits
All dogs over six months old must be registered with your municipality of residence. Licenses are issued upon presentation of an international vaccination certificate. Some cantons require you to take out liability insurance beforehand, so you will need to contact your municipality regarding this matter. You will be given an aluminum tag with the animal’s date of birth, license number and issuing canton. The tag must be fastened to your pet’s collar and worn whenever the animal is outside. Any dog found without a collar will be taken to a kennel, where an attempt will be made to find it a new owner or, failing that, it will be put to sleep. Game wardens have the right to kill dogs they find without collars.
Licenses must be renewed on a yearly basis by May 31. If you move within Switzerland, you will need to reregister your pet in the new municipality.
Dogs or other animals are not permitted in some lodgings (cats are not a problem). Contact your lessor for more information.

Etiquette
Dogs must be kept on a leash in public areas, although there are parks and other specially designated areas where you can let your pet run freely.
Some cities provide plastic bags to pick up after your pet. This is a gesture your community will surely appreciate.
Hooks have been installed in front of many stores to keep your dog tied while you are running errands.
Half-price bus fare is required for dogs. They are accepted in most restaurants.