Hi,
If the screen is broken it has to be replaced, as they are irreparable.
Here is a link to the ifixit guides on how to repair your phone.
[[Topic:Samsung Galaxy Note II]]
Here is link showing the cost of replacement LCD screens/digitizers for your phone, from one supplier. (''Ensure that you are looking at the correct model number'' when checking out the cost of a replacement). This is just shown to give you an idea of the cost. There are others if you search online using your ''model number and LCD replacement screen'' in the search term
http://www.etradesupply.com/catalogsearch/result/?warehouse=0&q=galaxy+note+2
If you find it too daunting to replace the screen yourself, I suggest that you contact at least three reputable, professional mobile phone repair services and ask for a quote for a repair to your phone. I recommend three, as this way you will have a better idea of the cost if all three quotes are close to each other in their estimated cost for the repair.