Sitecore does not seem to be using the version of a datasource that matches the current site language. I created a new version of a text-based item using the "translate" feature. This created a new version of the datasource under the "es-MX" category. I then set the current language to "es-MX" through the editing ribon. The page reloaded with a new URL:
mydomain.com/es-MX/path/to/page
However, I still see the English version of the datasource. Also, in the editing ribbon, the thumbnail above "Language" is still the US flag with the word "English".
Is there something that I am forgetting to do? This is on Sitecore 7.5
Figured it out. You have to make a new version of the page as well. If you try viewing your page in a different language whilst not in editing mode, it will display a page with the words "Default Page". This got me to try making a Spanish version of the page itself, not just the datasource present on it. After doing so, I was able to successfully change the page's language (thumbnail changed this time), and the datasource displayed its Spanish version.