While Satu gave the correct, Germanic pronunciation of "Undine", the more familiar pronunciation (no doubt due to the fame of the faerie tale by the Baron De la Motte-Fouque) is "uhn-deen". The name is alternately spelled "Ondine".
But, seeing as how the name was originally coined by the 16th century Swiss physician/alchemist/occult philosopher who called himself "Paracelsus", it was most likely pronounced by Paracelsus as Satu stated.
The Undines were one of four elemental spirits described by Paracelsus, being of the water. The other three elementals were: Sylphs (air), Salamanders (fire), and Gnomes (earth).
-- Nanaea