It's B-yerk! Not "B-york"!

Björk - is pronounced "B-yerk", not "B-york". The ö is voiced as "ur" and not "or". Think of it as the same way as pronouncing the o in "work" or "word".

Björk says to pronounce it like "Jerk":
http://b-faq.bjorkish.net/about/files/bjorkname.mp3

Guðmundsdóttir, her surname, sounds like 'Gvooth-moonds-daugh-terr':
http://b-faq.bjorkish.net/about/files/help%20with%20her%20last%20name.avi

Thanks to bjorkish.net for the clips!