So I got skyrim the other day and I put it in the disk tray to play it but it doesn't work; I click the skyrim disk icon to start the game up and it stays on a black screen, it doesn't move from this screen and the only way to get rid of it is to open the disk tray and then the console beeps twice.

I tried it today and still the same issue.
If anyone has had or knows of this issue and knows any potential fixes please reply
Thanks

Maybe is a problem of the bluray disc itself. try to go back to the gameshop and ask for a new Skyrim V copy.

Just go there: http://www.semperthree.com/ps3recoverymenu.html

And choose option 3...

3. Restore File System

...read the instructions of that page, how you do it. !!!

It should fix your problem.