Copy the URL of the paywalled article into the "I want to search the archive for saved snapshots" textbox! [blue, bottom box]
Can also archive an article for others to use if you copy a non-paywalled article into the "My url is alive and I want to archive its content" textbox. [red, top box]
-- Editing to add -- can also just append "archive.is/" to the beginning of the URL and it will take you to the list of non-parywalled, archived versions of the article