Original blogpost from Lobstergirl:
"Go to the page that shows all the quotes you like - the URL will be in this format - here is Otis's page as an example:https://www.goodreads.com/quotes/list/1
On your own page (not Otis's) over on the right you will see the link "export my quotes."
Otis is user #1. Insert your own user ID there. "Extra tips from MandyM:You can add the widget from your goodreads quotes to Booklikes. They will appear on your blog page. Each time you refresh the page it shuffles to a new quote. Just copy the widget from your 'My Quotes' page on Goodreads. Go to Booklikes. Click the Settings icon. Click on the 'Blog' tab. Click on 'Theme: Customise', then scroll down a bit till you see the 'Widgets Area' box. Paste the quotes widget there and save. I used Stylebot to put the font into 'bold'.