Change Fonts not working

I am trying to change the fonts on my website https://clermontfarmny.horseflydigital.com to be something other than the few basic ones and nothing I do seems to matter. Whenever I select a font from the drop down menu, it all looks the same on the preview and live site. The only fonts that seem to work are the basic ones – Arial, Georiga, Impact, Lucida, Myriad Pro, Palatino Linotype, Tahoma, Times New Roman, Trebuchet, and Verdana. All of the other fonts listed just don’t work.

How can I change the fonts to choose one of the other ones listed? Please help!
Thanks!
CJ