Google Reader will cease to exist after July 1. If you haven't migrated to another news reader yet, you only have a few days left before it's too late to export your data out of Google Reader.
If you're still hanging on to Google Reader, it's time to let it go. After Monday, Google Reader will no longer be available. People with only a few subscriptions will be able to migrate to another service without much hassle, but those with more than just a few will want the option to bulk-import the subscription data. Even if you don't move the data to a new service right away, it'll be nice to have for future reference.
To export your Google Reader data, follow the steps below:
Step 1: Go to Reader settings, then click on the Import/Export tab.
Step 2: Under "Export your information," click on the "Download your data through Takeout" link. You can also go to https://www.google.com/takeout/#custom:reader directly.
Step 3: Once Takeout shows 100 percent and provides an estimate of the number of files and size, click on the "Create archive" button.
Step 4: At the next screen, click on the Download button to download your Google Reader archive as a ZIP file.
Keep in mind that some Google Reader alternatives, like Feedly and Digg Reader, don't support importing subscriptions -- at least not yet. If you think you'll want to try either of those services, you might want to use their Google Reader import options while you still can.