Adding ajax to my plugin

I have been trying lately to develop a plugin. Now i want to add ajax function using jquery .

I already read and seen all the examples their in the net. and nothing helped me. I want to add the jquery to the public pages and not admin pages.

When i do so i jQuery.post(); and what i don’t know what goes in the url first argument.
i know that for admin pages it’s ajaxurl but if it’s public ?