same as
we're = We are

they've
Abkürzung von they have = sie haben

they've = they have = sie haben

(note: 'sie' is without a capital 's' in this case, because in this case it is meant to be is plural, and not 'Sie' with a capital 'S' what it would have been if it would have been meant singular)

'The recording industry won´t stop until they´ve shut down file sharing' = Die Musikindustrie wird nich ablassen bis sie die File-Sharing (Dateien-Tausch) abgeschaltet haben.

You can use the english term 'file sharing' in this context because it's a common used term, but it would use it with the capital letters, like they also do it on the following website, beacuse it is used in the german language this time.

Here you find the story about shutting down of Napster in german:

http://www.stern.de/computer-netze/readme/pflichtlektuere/ar...