The bell ringer ran rings around us, and the experience made me feel as if I'd been put through the wringer. I could have wrung his neck.
To ring something is to either make a circle round it; or to make it chime like a bell.
To wring something is to twist it -- either to squeeze water out of it by twisting (hence, a wringer as another word for a mangle; and also 'wringing wet'); or to kill something by twisting its neck.
Handwringing describes a gesture of powerless distress where the hands are clasped and twisted.
Wring someone's heart: hurt them emotionally.
Ring down (or up) the curtain on: To begin or end an enterprise (don't let those mean old subs make you change it to 'bring down (or up)').
Ring fence: This is a fence surrounding and sealing in a piece of land; but it is used in talk about funding and finance: "About £10m has been ring-fenced for research into HIV."
Ring the changes: This creeps into stories about... well change of any sort really. A writer who does this is wearing down the real meaning. To 'ring the changes' means to ring bells in a specific sequence which changes with every repetition. Be amazed -- check the Wikipedia article.