Click on this link.
If you’re not signed in to your Gmail account, you should see this window:
Log in using your Gmail account, and you’ll see a window something like this:
The left hand side lists some feeds that you’ve automatically been subscribed to:
Click on the BBC News one (or whatever is top of the list):
A yellow box like this will appear, probably. Click on the Dismiss this message link.
You’ll see a list of stories appear in the right hand pane of the browser:
Click on the top headline and another window will appear with the original story in:
You’re now reading an RSS feed.
You can play around with what Google Reader looks like by clicking on the Expanded view and List view tabs in the right hand side of the Google Reader window:
The List view will show just the headlines, while the Expanded view will show at least some of the text of the full post/story:
Try clicking on some of the other feeds in the left hand pane:
and on the Feed Settings button in the right hand pane:
Notice the Unsubscribe option. If you don’t want a feed in your collection, just have it open and then select that.
That’s it.