Hot to check if new posts have been published since page load and notify online users?

I want to show a div notifying online users that there are new posts since they have accessed the page, in the index and also if new posts have been added in the category or tag they are browsing.

I have been trying for hours to find a script that does exactly what I need, but I have not found anything exact, and my programming level is very low. Can anybody help me please?