Paying bills in Switzerland is a little different than the United States. First off, the Swiss don't use checks. This surprises a lot of Americans who use checks to pay bills and truthfully, it is kind of a pain in the butt. I still use my American bank account to pay student loans and storage fees in the US and I have to do a wire transfer to send money to that account.
There are some nice things about the system here though. For example, when one receives a bill, the company sends a slip of paper that has the account number, amount, and address of the receiver. It is standardized (and red!) and to pay, you just have to walk down to the post office, hand them the money (or use a bank card), and the post office transfers the money.
In the US, the mere mention of the post office would send shivers down my spine. This is Switzerland though and the post (pronounced: poscht) is much more efficient.
Another benefit: the post office also runs a sort-of bank so you can do all your banking business while paying bills. The only drawback is the post only deals with Swiss Francs and Euros. Oh well, it can't be perfect.