Here is a video overview of the service, including how to get started (the voice is kind of loud, so watch your volume):
Here are some other sites for getting started:
None of those guides is perfect, but they should all give you an idea. Here is my one paragraph guide for the super lazy and/or busy: Go to Google Reader and sign in using your Google account. If you are the last person in the world to have a Google account, now would be a good time to sign up. Now that you are in Reader, you want to add subscriptions. In separate tabs (if you are still using IE6, just give up and go home. Seriously) open up some of your favorite news sites and look for the RSS icon () or something that says RSS. Click on it to open a nasty looking text page (the feed). Highlight the URL and then go back to the Reader tab. Click on add a subscription and then paste the copied URL. Click "add" and then hope for the best.
Eventually you will get the hang of things and realize that there are different ways to do things, but that should get you going. One cool part of Reader is sharing. You can check your sharing settings under "Sharing settings." When you are reading an article or summary in Reader, at the bottom is a link that says "Share" and has a gray version of the RSS logo to the left of it. When you click on it, the logo turns orange and you have shared that article. The article then shows up in your public feed ("Shared items") and it gets shared with your friends. Here's a link to my shared items. That's it!
Alright, maybe the other guides are better. Oh well. Here are a couple of links for even more information: