EDIT: After publishing this article we learned of another article that gives additional information on what is probably the easiest method so far:
Yesterday, developer and programmer extraordinaire Erich Hoover and I spent several hours working out all of the Netflix Desktop kinks. Most users will have no problems with installation now.
Here is how to install the Netflix Desktop App on Ubuntu. …
Full details here:
PPA for Netflix Desktop App (iheartubuntu)
Should you have problems getting it to work, see:
Report Netflix App Bugs on Launchpad (iheartubuntu)
What follows is the original text of this post, which also mentions this method as one of the two choices:
Running Netflix is entirely possible in Ubuntu Linux 12.04 (and most likely any other modern distribution). See the section below “Running with Wine”.
Until recently there was no simple solution to watching streaming movies via Netflix (Watch Instantly) in Linux for any Linux distros besides Android based computers. Netflix has not released a player that will install natively in any of the others.
Read the full article here:
How to watch Netflix (Watch Instantly) in Linux (How To Wiki)