For Slick its very simple. LWJGL's applet loader will handle all the native stuff for you, you simply put all the natives for each platform in separate jars (like you'd do for webstart) and that applet loader will automatically only download the native jar for the platform its run on.

More detailed instructions for slick can be found in this thread. An easy way to create this is grab the example lwjgl applet package from lwjgl.org and modify it to fit your project. Briefly on gamejolt you upload lwjgl_util_applet.jar as your main jar and all the other jars as supplimentary files. Then you point to them using parameters so that the lwjgl applet loader knows where to look.

An added benefit of using lwjgl's applet loader is that it has support to use pack200+lzma compression on your jars, so that the download size is even smaller. Theres already about half a dozen slick applets on gamejolt.

I see that in Java 6 doc, pack200 seems to support only gz and not lzma. Am I right? If that's the case, which tool (link please) do you use to produce lzma?

Thanks for saving the day, Kapta! 

Multiple file uploading support is planned.

In the game website, you have to include http://

It now longer shows the game as you're uploading, so the process should be quicker now.