We are obligated to hear 100 shofar blasts on Rosh Hashona [source?] - how are those blasts calculated? Do we actually hear 100 or are there extra?
I think that this site http://www.chabad.org/holidays/JewishNewYear/template_cdo/aid/746659/jewish/Why-do-we-blow-the-shofar-so-many-times.htm sums up the computation -- what is important to remember is that a tri-blast like what we call a shevarim is considered "one unit" in the computation as is the truah which is often 9 staccato bursts -- one unit when computing blasts.
Dan's answer covered the "how are those blasts calculated?" part of your question; I'll do the other part, "Do we actually hear 100 or are there extra?".
We actually hear 100: 30 initially, 30 in the silent sh'mone esre (nusach S'farad and nusach Ari), 30 in the repetition of the sh'mone esre, and 40 (nusach Ashk'naz) or 10 (nusach S'farad and nusach Ari) in kadish "tiskabel". (I don't know what S'faradim do.)
However, Lubavitchers blow extra after "Alenu" for kabbalistic reasons, bringing the total to 130.
Blasts from the Past
The Rabbis developed the rule that there should be 100 blasts during Rosh Hashanah. The issue arises that, if there are nine blasts (biblically) how does one arrive at 100. Thus, prior to the Reader’s Kaddish, 60 blasts should have sounded. If there were nine blasts instead of ten, the count would be 56. See table below.
Shacharis (morning) Service
Torah 30 27
Reader’s Kaddish 40 44
Rabbi Ezra Bick of Yeshivat of Har Etzion, led by R. Soloveichik’s son-in-law, R. Aharon Lichtenstein) states:
Accessed 12/26/01. E-mail by email@example.com (Ezra Bick)
Explanation of the Sound of Shevarim
There are others who point to a commentary in the Talmud, Rosh Hashsnah 33b which points to
In Judges 4:22 we find in a battle involving the Prephetess Deborah during the itme of the Jusdges (prior to the establishment of the Israelite Kingdfoms in 1200) defeating the Canaanites in which Jael, another prophetess, entrapped a Canaanite General, Sisera, and killed him.
Judges 4:22 KJV
To explain Sisera’s Mother and her weeping., the Talmud (Rosh Hashana 33b) indicates that the sound of the teruah as translated as the Targum (Septuagint 130 BCE) translates the phrase as "yom yevava," a day of sobbing, based on the verse (Judges 5:28): "At the window Sisera's mother looked out, and cried." A Midrash (Yal’u’m Shim'oni on Judges 4:3), a codifed rabbinic teaching, tells us that indeed she cried (or sighed) 100 times! http://www.vbm-torah.org/rosh.htm
Issac Klein, former President of the Rabbinical Assembly confirms the 100 blasts:
Isaac Klein, Guide to Jewish Religious Practice, JTS, 1979
The conclusion is that tradition, derived from a rabbinic explanation of a Talmudic gloss, has taken hold in the custom of sounding the shofar 100 times on Tosh HaShanah.