(This is for those websites that have lots of different feeds. If you’re looking at a website with just a single feed, then check out this entry.)
Look around for a logo or something that says RSS.
This is what it looks like on Channel News Asia’s page:
In most cases clicking on this link will take you to a page listing all the available feeds. This is what the Channel News Asia page looks like:
Each website will probably look a bit different, so be a little flexible. What you need to do is to keep clicking on links until you find the feed you want. In this case, each of the links in the right hand pane will open another window in your browser (or a tab) with the page
If so, click on the right hand button Add to Google Reader:

You may now encounter a message like this (If not, scroll down until you find the message you do get):
(By the way If you’re not signed in to Google, then you’ll see this message)
(In which case click on the button, and enter your password if necessary)
and Google Reader will add to your collection of feeds, and return you to the page you were viewing before.
Or you may simply see a list of entries in your Google Reader with the line at the top You have subscribed to “Gadgets Page” or the name of the feed:

