Rosh Hashanah, The Jewish New Year, Begins Wednesday Night

The Jewish People begin the High Holydays on Wednesday evening, ushering in the year 5772 by starting nearly a month of special days: Two days of Rosh Hashanah on Thursday and Friday are this year followed immediately by Shabbat Shuva, the Sabbath of Repentance, and on Sunday by the Fast of Gedaliah.
Rosh Hashana is also the start of the Ten Days of Repentance which culminate with the solemn Fast of Yom Kippur on the tenth day of Tishrei. Special verses about repentance are added to the silent Amidah prayer said three times daily during these ten days.
This is Judaism's time for introspection, when Jews look back and examine their actions in the year that has just ended, seeking to improve their observance of the Torah’s commandments directed towards G-d and towards their fellow man. They are expected to ask forgiveness from those they may have offended or hurt during the past year.
On the Sabbath of Repentance this Saturday, a special chapter is read from the book of the prophet Hosea, calling the Jewish people to repent and return to G-d. Rabbis traditionally deliver a sermon, drasha, on repentance in the afternoon.
The Fast of Gedaliah commemorates the end of Jewish rule in the Land of Israel following the destruction of the First Holy Temple some 2,500 years ago, prompting the sages to say that the end of Jewish independence is comparable in solemnity to Yom Kippur.
The Jewish New Year has several names, among them the Day of Judgment. It is a time for careful stock-taking of one's relationship with G-d, and the longer Rosh Hashanah morning prayers filled with emotion, responsive readings and songs, are therefore intense and inspirational – usually led by a carefully chosen cantor or member of the congregation - concentrating on G-d's Kingship, eternal presence and His judgment of all creatures. 
“Repentance, prayer and charity avert the evil decree” is a central line from the Machzor, the special holiday prayer book, listing the course of action that it is hoped will lead to meriting a good year.
Upon returning home after the evening prayers, symbolic foods – simanim - are served, whose names allow a play on words that ask for our merits to be numerous, for our enemies to be destroyed, that we lead rather than follow. There are especially sweet ones, such as apples dipped in honey, to symbolize a sweet year.
Fruits that require a special Shehecheyanu blessing, said for something new, because they are being eaten for the first time since the previous season, are served on the second night.  Pomegranates are often used for this purpose. Traditionally, children wear a new garment for the first time the second night and can say the blessing. Candles are lit both nights, but it is forbidden to light a match on the holiday, so an existing flame is used to kindle them.
Based on the commandment in Numbers 29:1, 100 shofar blasts are dramatically sounded throughout the prayers, "awakening" us to improve our ways.  The congregation refrains from speech from the first shofar blasts until the last ones at the end of the service..
The Tashlikh prayer is recited on the first afternoon, preferably near a live stream of water in which we ask G-d to "throw away" our sins.
Many religious Israeli youth spend the holiday at secular kibbutzim to lead the services, volunteer to lead services in the IDF and in hospitals. Breslover Hassidim and others have begun a custom of  going to Uman, Ukraine, to pray at the gravesite synagogues of their spiritual leader, Rebbe Nachman of Breslov, who passed away in Tishrei of 1810.  Prominent rabbis, however, oppose the idea of leaving the Holy Land to spend Rosh Hashana in the Diaspora.
Five days after Yom Kippur the holiday of Sukkot begins, which in Israel, is seven days long, but is two days longer in the Diaspora, culminating the month of holidays.