Practice, practice, practice.

I don't see how it could matter what song you choose to sing ~ as long as it's something you enjoy enough that repetition doesn't become unpleasant to YOU.

(I suppose that a song with plenty of built-in demand for an extended range, like "The Star-Spangled Banner," might be extra-effective, buit anything will work if you step it up through enough different successive keys.)

I'd like to add my personal experience that vocal range CAN definitely be extended if you keep on singing. I think that it's necessary to overcome all your inhibitions; if you're timid, or even just trying not to be too loud, you won't be able to extend your range ~ not by much, anyway. If you really hope to start reaching higher (or lower) notes than ever before, you have to be ready to really let loose.