Google shutdown the Google reader service from July 1 2013. You will have to switch to other alternatives.
You can take a backup of your Google Reader Subscriptions Data before 15th July 2013. So please take a backup of the data if you don’t want to loose it for ever.
Here is How to
1. Go to Google Takeout and login to your Google account (if you don’t have logged in)
2. Choose “Choose the services”
3. Click Create Archive and wait till it finished
4. Download the zip file after the completion
You can extract the zip and find the “subscriptions.xml”, which can be used to restore your feeds to other Google reader alternatives.
these links may help you to find an alternative
Google Reader - What are the alternatives
AOL Reader an alternative for Google Reader