I am trying to have a looped task for a To Do item that has to happen for a member of the team, how do I make that happen? So in essence, when it is done, we need to start again from the beginning?
However, if you want to clone/copy cards in the meantime and are using Google Chrome to access your Trello boards, there is a Chrome extension called "Trello Clone" which can perform this task for you. Sometimes, you have to refresh the page for the clone options to come up.
I've been using this extension quite happily for several months. I just clone a new card for each iteration of the repetitive task.
EDIT: The Trello "Card Copy" feature went live as on June 15th. The official blog post explaining the changes is here.
There's no way to add recurring tasks at the moment.
The team is finishing work on card copy, which may be similar to what you want. It allows you to create new cards based off old cards, with the same checklists, member, attachments, etc.