I agree that it is quite old-fashioned and unlikely to be used in day to day speak! (I'm from the UK).
You may read it in novels, or perhaps in a satirical context it could be used... perhaps as a sarcastic response you could say you're 'giddy with delight' or 'giddy' at the prospect of something.
It's similar to being dizzy, but 'giddy' is quite a quaint and fairly dated way of expressing that feeling.
Similarly, to describe someone as 'giddy' means they're a bit scatty, excitable, perhaps all over the place, a bit 'dizzy' or unreliable and child-like and bouncy, but again it's not something you'd really say these days. I can't remember the last time I heard, read or used the word!
Hope that helps!