Your link to Wikipedia on the Hebrew calendar is an excellent link and contains most of the data you need. An overview goes something like this:
The day begins at sunset and extends until sunset the following 24 hours. The day is divided into 2 x 12 hours.
The week begins, as almost everywhere on what we call Sunday and ends on the Sabbath (Saturday). Friday is called the day of preparation.
The month begins with the new moon and extends to the next new moon. This means that each month has either 29 or 30 days and so the year has about 354 days.
Because the 12 months of lunar years has only 354 days (on average), an extra month must be added every so often; specifically 7 times in a 19 year cycle to keep the solar year correct.
Several starts of the year are known and were variously used at different times of history. Months were numbered from Nissan when the Passover was celebrated in the first month about our March/April. However, a civil calendar is also used that starts in the seventh month that contains Yom Kippur.
Three main festivals are celebrated:
- Passover & unleavened bread
- Trumpets, Atonement & Tabernacles
For details of these festivals see Lev 23. Later, other festivals were added such as Purim and Hanukah.
There is much more information and references in https://en.wikipedia.org/wiki/Hebrew_calendar