How can I get the rights to my final year project?
The first question is why you want the rights.  For example, if you are working on something with serious commercial applications and hope to start a company or sell the technology, then this is a very serious issue.  The first step is hiring a lawyer, who can advise you on precisely which rights you and the university currently hold, and who can help you negotiate with the university regarding commercialization.

On the other hand, most student projects are of no commercial value.  If you just want to display your work online (to help build a portfolio for job applications and in case this work is useful for someone else), then it's probably easier.  It may depend on the university, but presumably they don't want to limit the dissemination of student projects, so if you ask them I bet they'll grant permission.  You should think about exactly what you want to provide and under what sort of license (for example, if you put code on the web, nobody's allowed to use it unless you license that).  I imagine the university would be happy with some sort of Creative Commons license.

I'd recommend being very clear and straightforward when asking, to avoid raising suspicions that you are trying to trick them into giving up the rights to valuable technology.