How do I ask / inform my supervisor that I need to take a day off?
XX,

I was just given a surprise gift -- tickets to a show in YY City.  It would be thrilling to go -- any chance you could spare me on Thursday?  Because of the distance, it would mean missing the whole day.  However, I'm free all day Saturday.  If you like, I could come in then to make up the time.

(however you like to sign your name)

Please feel free to adjust this as needed.  For example, you can make the tone less breezy and more formal if you want to.