how to display a list of OG content depending on user group membership?
There is a pretty good tutorial of OG at https://drupal.org/node/1603460. 

If you already know the basics and have provided proper access fields using the Organic groups access control module, you should next explore the views that come with OG and edit them to your liking.

Also the OG Extras module at https://drupal.org/project/og_extras has lots of stuff for practical use.