To encountering this epic cool guy you have to go to the mysterious door in Snowdin and move around in that room for at least 3 minutes.(make sure you have not fought with papyrus yet or else Glyde wont appear)

To spare him you have to applaud twice and do nothing three times try to dodge all of his attacks.

if you have successfully done he will run away after the 3rd try of you doing nothing (you monster)