How can I recreate the text effect in the image below, including shadows and borders using HTML5, CSS3, and Google Text API (if needed)?

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There are many ways to recreate the graphic. You could absolutely position the elements, or you could let the elements flow into place nicely.
For the latter, which I prefer, you need a container for the image (as background), a container to hold the text (which will have a semi-transparent background) and then the text itself, broken up into inline/inline-block elements so you can style each.
Here’s how I would do it using inline-block to layout the text appropriately and changing the fonts/font-sizes/padding for each text element (including google text API):
JS Fiddle: http://jsfiddle.net/rgthree/v6h2g/
Obviously, I didn’t try to mach the font itself.