Reeder is a Google Reader client, which means you need a Google Reader account to use the app.
Don't have one? No problem, you can get one here:
When using Reeder, all changes will be synced with Google Reader. This means if (for example) you read an article in Reeder it will also be marked as read in Google Reader. The same is true if you read in Google Reader. When syncing the next time, Reeder will just pick up the changes.
Please note: Managing subscriptions inside the app is not (yet) supported. For now, you have to do this in Google Reader.
The filter control lets you easily switch between different views on your subscriptions: Only show starred items Only show unread items Show all items
Grouping options for article lists: Group by date Group by feed
Other: Mark all as read
A note regarding the sync button: When done syncing, Reeder will cache embedded images of the articles for offline reading. The circle around the button indicates the progress of the image caching.
Having issues signing in with your Google Apps account?
Some users reported that changing the password did the trick. If this does not help, enabling 2-step verification and creating an application specific password should get Reeder working again. Please see this help article (Getting started with 2-step verification) for more information.