We want to be working locally while working on this project. Just a few reasons:
We can work offline from anywhere.
We're working on a complete redesign that will take many days, we can't leave a live site half-cocked.
There is no risk working locally.
We can use version control, giving us a record of what changed when and making future team work easier.
We can use preprocessors.
To work locally, we use MAMP to create a local domain name with a local folder as the root. We use Sequel Pro to create (and manage) a local MySQL database. We download and install a fresh copy of WordPress and install it. We export all the posts/pages/comments/attachments and stuff from Jeff's live site and import it locally.