After all that, I hope you're ready to make the changes. If you've never made any changes to your template before you don't need to worry about ruining your site as Blogger has a "Revert widget templates to default" link. If things go kablooie click on the "Revert widget templates to default" link and everything will go back to what it was.
If you have made changes before then I assume you know that you need keep a back-up copy just in case. Otherwise the "Revert widget templates to default" link will erase all your previous changes.
First thing to do is to make certain that you like the class name. I think it is good practice to use descriptive names. In this case "sideRight" or "sideLink" or what-have-you. If you want a different name go back into LAYOUT > EDIT HTML and change the name of your style.
Then you'll have to add the class name to all the links on the right side. Don't worry if you have lots of links, you won't have to make many changes. HOWEVER this will probably be your first forray into changing server-side scripts so it will be a little different than what you're used to.
To test this out and to give yourself confidence to a CTRL F (to find information on a page) and type in "href" in the text box. You will probably have two matches. Go and verify that for yourself. Now select "Expand Widget Templates."
Here's where the confusing part comes in. You have to find the correct href to make changes too. If you're labeling your widgets you'll have an easier time. For my first few changes I searched for the WIDGET label, then it's easy to see where to make the change. The first image shows the text as I found it. The second one with the class added to
You'll see that I called the style "side". I did that to keep all the code lined up from image to image. Side is a bad name. It's not descriptive enough and there are too many "side" to do an efficient search. "sideRight" is a far better name.
Remember, after you make a change. Save it, take a look at what you've done. You can always reverse it later.