What is your system for paying bills?

I am taking over full responsibility for paying my household bills next month and thinking about how to set things up. Obviously can pay bills by handwritten check and may do so but want to know more about online banking. Is there a difference between automatic bill pay and EFT? Who do you set it up with – the bank or the company? What about paying by phone? I have set up an online account at my bank but not any bill paying as yet. Most of the household bills have been coming out of another account thus far. Am polling a number of people to get ideas.