How do I find the secret library .. it is the last room to complete in my apartment.

You get it once you reach level 50. it is a bookshelf that you get in 3 pieces.
once complete you place it in a room and click on it. it will open.
click on it again and go in.

Hey If I remember well you start to gain the 1st piece of Mystery Bookshelf at level 23 then you have the complete one at level 30 and once you have achieved that level you will find the Bookshelf in your inventory, place the bookshelh where you prefer in one of your homes and then start to decorate

here is a link where you can find all levels and what you will get for each one
http://yoworld.wikia.com/wiki/Level