Final warning, the Google Reader service shuts down Monday, July 1, 2013. If you haven't already this weekend is your last opportunity to download your subscriptions. Even if you haven't decided which alternate service to use or if you even want to continue using RSS, it's a good idea to go ahead and download your data. These files are small and will give you options in the future. Here's a quick tutorial explaining how to download your data from Google Reader.
Visit Google.com/takeout and sign in to start the process to download your data.
Choose Your Services
You can choose to download data from all your Google services, or just select specific services like Reader.
Choose Data to Download
If you're just choosing to export specific services, select the services you want to export. I'll just choose Reader in this example. Then click Create Archive
Download Your Data
Your data will be prepared for download in a zip file. This can take a few seconds or several minutes depending on the amount of data you have to download. Once complete, download the zip file to your personal computer.
Find and Expand the Downloaded Zip File
The zip file should expand automatically when opened.
Find the subscriptions.xml File
Inside the zip file you will find a folder for the content you downloaded. There should be a folder for Reader with a "Subscriptions.xml" file. This is the file you will want to save and import into your new RSS service.
Find an Alternate RSS Service
Google Reader Shuts Down July 1. For an overview of the various alternate services and options, check out last week's Mac Power Users Podcast, episode 143.