I stumbled on your post as I'm having the same issue. Nothing is broken in the web application I'm building but the fonts don't change to the beautiful fonts being used at semantic-ui.
Upon searching a little more, it seems that semantic-ui does not define any base font settings, at least for now. Have a look here. Custom package creation is still being added. Until then I guess you need to let your inner web designer do the due!
Update:
I poked around a little more and was able to get the fonts being used by semantic-ui. Go to Google Fonts and create your own font collection. Semantic-ui is using Open Sans. Click the use button at the bottom to get the link to the font style sheet in the 3rd step. For Open Sans, the link is:
<link href='http://fonts.googleapis.com/css?family=Open+Sans' rel='stylesheet' type='text/css'>
Include the above line in your <head>
tag and then include the following <style>
tag.
<style type="text/css">
{# set default font for website #}
* {
font-family: 'Open Sans', sans-serif !important;
}
</style>
You should be all set!