Summarize:

Anyone new to Switzerland who hopes to open a bank account there will need to meet with a bank representative. It's best to make these arrangements and get a bank account set up as quickly as possible. It may be helpful to visit a Swiss bank branch before you close out your old bank account from the country you're leaving, if at all possible. Some expatriates may have a difficult time securing their housing without a bank account, yet they may also have a difficult time opening a bank account without an address. Potential customers living outside of Switzerland who wish to open a Swiss bank account but cannot visit a branch in person may be able to request an application package by mail. Documents provided by the potential customer will need to be authenticated, either by a notary, an employee of the Swiss bank, or an employee of a correspondent bank that the Swiss bank is willing to work with. Most Swiss banks assign a personal account manager to work with each customer, and it's important to remember who your account manager is for all future bank transactions. Ask for your account manager's contact information, including his email address and direct phone line at the bank. Bank branches in major cities tend to have at least one account manager who speaks a foreign language, including English. Otherwise an account manager will most likely be fluent in one of Switzerland's four major languages: German, French, Italian, or Romansh. If you know you will require an account manager who speaks a language other than the major languages of Switzerland, it's best to call ahead and make the necessary arrangements. Like most banks and financial institutions around the world, new customers wishing to open a personal account will need to provide documentation that proves the customer's identity and source(s) of income.  New customers will be asked to verify their identity and address. If your identification card does not reflect your local Swiss address, you may need to provide a signed copy of your lease. Some banks will require a new customer to verify his professional status. Banks may also require new customers to show any relevant work contracts and tax returns as part of the employment verification process. Showing proof of employment helps banks know that the money being deposited into an account has not come from illegal activities. There are over 20 Swiss banks that are cantonal, meaning they only do business with residents of the canton in which each bank is located. If you open a personal account with a cantonal bank and move to a different canton, you may be asked to transfer your account to a corresponding canton. This should not be a problem for customers who open accounts with Swiss national banks. Most Swiss banks charge a monthly maintenance fee for personal accounts, and may charge additional fees for a credit card or Carte Maestro (debit card).  Monthly fees for personal accounts tend to range anywhere from 10 to 30 Swiss Francs (CHF), though customers can usually have these fees reduced or waived by switching to electronic banking statements, taking out a mortgage with the bank, or depositing a sizable amount of money into that account.  Credit cards and Carte Maestros tend to have annual fees that range up to 3 Swiss Francs.
Visit a bank branch or representative office. Get assigned an account manager. Provide the necessary documentation. Learn cantonal requirements. Expect to pay charges and fees.