Here are some options for Audio Books. I personally prefer the first 2 versions. There is yet another version which is the best but that of course is not free. Hear the wikipedia version or the gotham radio theatre version. If not the whole thing do listen to some parts of it - like the first conversation between Lady W and Duchess of B and the conversation between Lady W. and Lord W to start with at least. And the part where Mrs. E enters.
http://www.nypl.org/audiovideo/gotham-radio-theatre-presents-lady-windermeres-fan
http://en.wikipedia.org/wiki/File:Oscar_Wilde_-_Lady_Windermere's_Fan_-_Act_I.ogg
http://en.wikipedia.org/wiki/File:Oscar_Wilde_-_Lady_Windermere's_Fan_-_Act_II.ogg
http://en.wikipedia.org/wiki/File:Oscar_Wilde_-_Lady_Windermere's_Fan_-_Act_III.ogg
http://en.wikipedia.org/wiki/File:Oscar_Wilde_-_Lady_Windermere's_Fan_-_Act_IV.ogg
http://archive.org/details/lady_windermeres_fan_1002_librivox
http://www.nypl.org/audiovideo/gotham-radio-theatre-presents-lady-windermeres-fan
http://en.wikipedia.org/wiki/File:Oscar_Wilde_-_Lady_Windermere's_Fan_-_Act_I.ogg
http://en.wikipedia.org/wiki/File:Oscar_Wilde_-_Lady_Windermere's_Fan_-_Act_II.ogg
http://en.wikipedia.org/wiki/File:Oscar_Wilde_-_Lady_Windermere's_Fan_-_Act_III.ogg
http://en.wikipedia.org/wiki/File:Oscar_Wilde_-_Lady_Windermere's_Fan_-_Act_IV.ogg
http://archive.org/details/lady_windermeres_fan_1002_librivox