1. I added feeds to my reader directly from the website by clicking on the RSS button. This is the easiest way I find to add them.
2. The "Add a subscription" button on Google Reader is another easy way to add a feed. Click the button and type the URL of the website (not even the feed usually) and it will add that sites feed to the reader. This is a good way when you cant find the RSS button on a website.
3. Recommended Feeds. Google Reader will examine the feeds you currently subscribe to and recommended to you new feeds based on what you already follow. This is a great way to discover new sources.
I prefer using an RSS reader to visit my favorite sites. All of them are all in one place and I can see if they have been updated or not since I last looked without clicking. However sometimes the author does not post full articles to their feed, in which you will just click through to their website anyway to continue reading.
I find this technology useful because it centralizes my news reading life into one place; not into 20 clicks through my bookmarks.
A web based RSS Reader is better because I can access it from any browser. So if I'm at school or traveling, I can always access my reader. If I was using desktop software, I could only use it from the computer I have it installed on.