I get a bill. At the bottom of the bill is a red pay-in slip with a magic number on it. I log in to my bank, enter the number, tell it how much I want to transfer, done.
There's a not-used-enough automatic system where one of my creditors can send their bills directly to my bank. Now, I log into my bank, get told there's a pending e-bill, at which point I select it, press 'pay', done.
No fees anywhere.
I'm from the UK, which is just starting to do this, but it's nothing like as polished; small traders and tradesmen still prefer cheques, and regular payments are typically done via direct debit, where you authorise them to debit money directly out of your bank account (with a whole pile of banking guarantees). Switzerland seems to do this much less frequently; most people just pay the invoices monthly.