Basically, if you have a Gmail account, you have Google Reader. There is a little series of links at the top of the page where your Inbox is that says "Gmail Documents Photos Reader" etc...
When you're on the homepage of a blog you read, you should see a little square with 3 lines like radiowaves coming out of it, at the right side of the bit where the web address is (this is a very technical description as you can see
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). If you hover over it, it should say something like "Subscribe to this page". If you click it, you'll get options of where you want it to subscribe to, Google is usually the first option for me. You select Google and then it will ask you if you want it to appear on your Google Homepage or on your Google Reader. Choose "Reader" and then that's you subscribed.
Just click on your Reader link when you're logged into your Gmail and you'll be able to read all the updates of your blogs without missing a single one.
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It may vary from browser to browser, but that's how it works for Firefox, for me anyway.
ETA: I just noticed we have the little "Subscribe" boxes on this site, little orange ones next to every forum title, if that helps to illustrate my poor description.
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