If you want the instant streaming option, you do need an internet connection with at least 500kbps (0.5MB) speed. (kbps = kilobits per second) You might be able to use a public wi-fi network (for example, at a Starbucks) but you might not get the bandwidth to keep the movie going. Netflix also has a DVD-only option, http://dvd.netflix.com/
, which doesn't require a high-speed connection. (You do need enough access to the internet to select movies for your movie delivery feed but using a library computer's network access might be enough.)
Note: if you use a public wi-fi network, you are at risk of someone sniffing out your Netflix password. Make sure that the Netflix password isn't the same as your password for any other account that you have.
I hope this helps.