To place a widget on your site, pull an 'embed' element onto the site that you want the widget to appear. Then, go to the site offering the widget, copy and paste the code that they give you and enter this into the 'embed' element. Voila'! You should see the widget appear once you click outside of the element. My new favorite is an RSS Snippet feed widget that allows me to display a portion of my blog (or another feed) anywhere I'd like! I recently did this for a customer in D.C. in her footer so that it appeared on everypage. It just lets the end user see a snippet of a blog and allows them to click on it to see the rest of the posting.
For example, I have put one on my Plain & Simple Web Design site that looks like this:
Now, for the warning. It can get pretty addicting once you start finding widgets. A couple are okay, but too many can make your site start to look like a hot mess and become distracting. Ask yourself, "Why am I adding this widget (or Plug In)? Don't add them just because you can or because you saw it on a competitor's site. Your new widget should serve it's purpose, which is to promote your site and what you're selling! I like my blog snippet widget and mail list widget in my footer because it doesn't dilute the purpose of my site which is contained in the main content of my site. Be smart and strategic with everything that goes on your site. In addition, all those widgets require loading, so check your site live and make sure that the widgets you use aren't slowing down your load time.
All in all, a couple of well placed widgets can enhance your website brand and purpose, but remember to keep them in check and don't get carried away.