Today's date in the Jewish Calendar is:
1-2 Rosh Hashanah (Jewish New Year)
10 Yom Kippur (Day of Atonement)
15-23 Succoth (Feast of Tabernacles)
15-22 Pesach (Passover)
The Jewish year count dates from a traditional date for the creation of the world.
The Jewish calendar is based both on solar and lunar cycles, with the lunar influence predominating. Each month in the Jewish calendar is 29 or 30 days long, which approximates the lunar month. Twelve of these lunar months total 354 days, about 11 days short of the solar year. This leads to a substantial drift from year to year of specific dates relative to the solar year (although all holidays occur on a fixed Jewish calendar date). To correct for this, an additional month (Adar II) is added during leap years which occur roughly every third year. In addition, other changes are made every 19th year.
After correction, the length of the solar year as defined by the Jewish calendar is short by about four minutes a year, which means it is about four and a half days off per millenia.
The Jewish calendar originally depended on the actual time of observation of the new moon, much like the current Islamic calendar. All decisions about the calendar were made by a committee of the Sanhedrin (the Supreme Court in Jerusalem), the Sod Haibbur. This committee calculated the dates of the beginnings of the months and the seasons based on astronomical observations and calculations, as well as meterological and agricultural considerations. They determined when the intercalations would occur, that is inserting periods of time into the calendar to meet religious requirements and to keep it in synchronization with the solar year.
After the destruction of the second Temple in 70 C.E., the maintenance of the calendar gradually passed to local synagogues. The decision-making process was decentralized, which led to the possibility of holidays being celebrated at different times in different localities. This led to the practice of extending some of the holidays to ensure that all Jews could celebrate them at the same time, for instance, adding an eighth day to Passover.
For this reason, in the fourth century C.E., the Patriarch Hillel II decided to codify the rules for computing the calendar, which fixed the method of computing the calendar to the current algorithm.
The only day of the week with a name is the seventh day, the Sabbath. The rest are numbered rather than named.
The day is divided into 24 hours of equal duration. Each hour is divided into 1,080 helek (plural, halakim). Each helek is divided into 76 rega (plural, regaim).
The day begins and ends at sunset for religious purposes. By this reckoning, midnight is hour 6 and noon is hour 18. For calendrical purposes the day begins at 6 p.m. Jerusalem time.