My task is to create a simple web browser in Java. So far it can only read HTML pages. I'm using standard JEditorPane component to display webpages.
Now I was wondering is there any way you could explain me how can I manage to display at least some simple pages that contain CSS/Javascript. If you could point me to some useful links or appropriate examples I would be very happy.
Well, my advice would be to look at open source rendering engines such as Gecko - https://developer.mozilla.org/en/Gecko_FAQ
You can embed Gecko with Java using the JREX library - http://jrex.mozdev.org/
Starting from scratch with a problem like this is a very big task, and as your username is AmateurProgrammer, I wouldn't recommend it.
There alrady is some prior art for the Java browser segment.
concerning javascript, you will have to use a javascript interpreter in Java. A renowned one is Rhino (by Mozilla). Its integration may reveals to be an interesting challenge.
concerning CSS, it seems the question has already been asked ...