ועתה ישראל מה ה’ אלקיך שאל מעמך כי אם ליראה את ה’ אלקיך ללכת בכל דרכיו ולאהבה אותו ולעבוד את ה’ אלקיך בכל לבבך ובכל נפשך” (י’,י”ב)
The Gemara in Menachos (43b) derives from this passuk that one is obligated to recite one hundred berachos every day. Rashi explains that the word “מה” is read as “”מאה” one hundred. Rabbainu Tam explains that there are one hundred letters in the passuk for the word שואל is with a vov.
The Midrash Rabah (Parshas Korach 18;21) says that in the days of Dovid Hamelech there was a plague in Yerushalayim and every day one hundred people died. Dovid Hamelech instituted the recital of one hundred berachos and the plague stopped. The ספר המנהיג explains that this takanah was really from the days of Moshe Rabbainu which over time was forgotten. During the plague, Dovid reinstituted it.
The מחבר (או”ח סימן מ”ו סעיף ג’) writes חיב אדם לברך בכל יום מאה ברכות לפחות” – A person is obligated to recite at least one hundred berachos every day. The Mishnah Berurah makes the calculation of the one hundred berachos that we recite daily as well as Shabbos and Yom Tov. The שבט הלוי and Reb Shlomo Zalman Aurbach zt”l are of the opinion that women are not obligated in this mitzvah. Many of the berachos listed by the Rishonim that are part of the one hundred are not applicable to women. For example; tzitzis and teffilin and all the other mitzvos that are זמן גרמא. Both Reb Elyashiv and Reb Ovadia Yosef zt”l are of the opinion that women are obligated in this mitzvah. They need to make up the one hundred with other berachos.
The Rishonim and poskim start calculating the count of the berachos from the night – צאת הכוכבים, similar to everything else in the Torah that starts at night. If one davened Maariv after פלג המנחה on a regular weekday, the poskim are not sure if those berachos are counted for the following day or not. Do we say that because he davened maariv it is already night for him, or since for mitzvos, for example – krias Shema, kizayis of matza, kezayis in the sukkah – it still has a halacha as day, it is still counted with the previous day’s berachos?
However on Erev Shabbos many poskim rule that since when davening early he is accepting the Shabbos, and he can even make Kiddush and eat his seuda, it is considered Shabbos for everything including for the one hundred berachos.
The same would apply to Motzai Shabbos, until after birchas hamazon of Shalosh Seudos, these berachos are calculated with the berachos of Shabbos since it is תוספת שבת. However many poskim still hold that the calculation is only from צאת הכוכבים to the following צאת הכוכבים, therefore לכתחילה one should be careful to calculate his berachos in this way.
On Shabbos when we are missing many of the one hundred berachos one is obligated to make them up by making berachos on fruit and other delicacies. The Gemara in Menachos says that on Shabbos and Yom Tov רבי חייא would make up the berachos with smelling בשמים and on eating מגדים. This is the source to have a “Shabbos Party”.
The Brisker Rav zt’l is of the opinion that if one knows ahead of time that he will not be able to reach one hundred berachos, there is no ענין to try to make as many berachos as possible. The Brisker Rav would take the aliyah of maftir on Shabbos and Yom Tov to make up the one hundred berachos with the berachos of the haftarah. On Yom Kippur however, when he anyways was not able to recite one hundred berachos, he would take the aliyah of Levi.
However Reb Aharon Lieb Shteinman zt”l and Reb Chaim Kanievsky shlit’a both hold that one should still make as many berachos as possible. Reb Chaim brings a proof from the רמב”ם (פי”א מהלכות ברכות הט”ז) who says “יזהר אדם בברכה שאינה צריכה וירבה בברכות הצריכות” – one should make as many berachos as possible. At the same time one should not be making berachos that are unnecessary to try to reach the number of one hundred berachos.
Prepared by R’ Avrohom Yehoshua Ziskind
 Sources;דרשו,פסקי תשובות,אילת השחר