They will send a confirmation email. After you click the link to confirm, it says "We will provide your information to you as soon as we can. Usually, this should take no more than a month."
EDIT: you can export your book database as CSV (shelves, ratings, reviews, etc) here https://www.goodreads.com/review/import (there's a link towards the top to export...disregard that the URL says "import".
Can it reasonably take a month to export the data from Goodreads? I barely use it but from what I recall its basically lists of will-read and have-read right?
Is that delay strictly a "cooling off" sort of tactic?
I assume this data export includes much more than just the book data (which I just discovered you can get immediately as CVS via https://www.goodreads.com/review/import) which might be part of a compliance requirement.
Update: I got an automated email from Goodreads to download this export. It contains a bunch of json files containing user/usage-related data for my account like request logs, newsfeed updates, kindle logins, site settings, etdc.
Hopefully not, maybe someone should scrape everything from there. I didn't know amazon owned book depo, maybe I should have guessed something has changed when they starting sending increased number of marketing emails a year or two ago.