Payphones are owned by Swisscom and you will have no difficult in finding one. Few takes coins nowadays (except those at airports and big railway stations) so it's advisable to have a phonecard, which you can buy at the numerous kiosks or post offices. You can also use your credit card to make a call.
If you're staying in Switzerland for a longer length of time, it would be advisable to buy a SIM card for your mobile phone. Three companies offer these: Swisscom, Orange and Sunrise. The best offers can be had if you buy your card through a supermarket, either Migros (Swisscom) or Coop (Orange). Phones can be rented, this is possible at the airports.
The International Direct Dial Code is 00. This is the access code you use "within" Switzerland to dial an overseas number ( or make an overseas call ).
41 ( four one ) is the International Telephone Country Code for Switzerland.