I’ve just begun using Google Reader.
At the top left of the page, click on “Add a subscription” and type the blog or URL which interests you, for example: http://www.christian.org.uk/ for the Christian Institute.
If you repeat this for your favourite blogs, then you will be able to run through the headlines for all your blogs on one page on Google Reader. You are only one click away from that blog or website if you want to investigate anything further; but often you just keep scrolling down the page till you see an item that interests you.
Google Reader marks them so you can see the new ones without difficulty.
1 Jul 2013: Google Reader was officially retired and discontinued today.