You just transfer the money from your bank account to the bank account of the merchant. There are various methods to do that, I prefer giropay[1]. If it's a merchant you regularly use like amazon you allow the merchant to directly withdraw[2] the money from your account.

It's not like this is some weird highly advanced stuff. Surely that's possible in the US as well?

[1]: http://en.wikipedia.org/wiki/Giropay [2]: http://en.wikipedia.org/wiki/Elektronisches_Lastschriftverfa...