Jerry - The additional service is called Musaf and is part of Conservative and Orthodox services. I don't know about Reform and Reconstructionist. It is usually right after the rabbi's sermon and the Torah scrolls get put away. The congregation says the Rabbi's Kaddish, then says the Amidah, then the Amidah is repeated, (it's during the repetition that the Kedushah is said in response form by the congregation and the leader/chazzan/cantor/rabbi/whoever's running theshow), then Eyn Keloheynu is sung, and on we go until Adon Olam and by golly it's time to eat and we're more then ready, ey?
The word ends with a BEGINS with shin - no right to left jokes, please - then nun then yud, then suf/tuf.
I have a friend who has a Hebrew songbook containing various traditional songs for piano with guitar chords I think. I'll try to get the name.