Typecase is a web font management plugin that allows you to browse, search, and embed over 500 fonts from Google Web Fonts.
Once you install one of these plugins, use the inspector tool to be able to hover over and click on different page elements like h1 (a top-level heading element) or p (a paragraph element).
Once you find the element you want to target, you will add a new "Selector" for the font you've added to "Your Collection." In the "Selectors" sidebar, simple enter the element like so: "h1" or "body" or "article" (this is a new HTML5 element).
To target certain parts of the page that may use an ID or class name, you would enter "#id" or ".classname" to target those sections of the page.
Well, this is a problem. Your theme probably sucks and is applying the "font-family" CSS declaration to something in a non-graceful way. My recommendation is to "cascade" your styles by using extremely specific selectors so that you override your theme's naughty CSS by selecting "html body #id" or something to that effect.
The plugin fetches the latest list of fonts from Google every time you edit your fonts, making it easy to grab the latest and greatest web fonts Google has to offer.
We're currently looking into it and would love to be able to provide a much larger font selection as soon as possible. As for right now, we have not begun building that piece out yet.