Code:
<applet width="640" height="480" code="com.mojang.mario.AppletLauncher" archive="mario_01.jar">
</applet>
This is how they call it on their page. I'm not sure how you would upload the files, though, as I am not well versed in Java applets.
I would assume (but don't quote me) that you just unarchive the .zip file onto your web site recursing subdirectories, then insert the above snippet into your site. I could very well be wrong, however.