Jewish Festivals are listed in the Torah and are of two types: 

1. Three pilgrimage festivals (shalosh regalim):

• Passover,
• Shavuot, and
• Sukkot (including Shimini Atzeret).

These festivals were celebrated in ancient times by "appearing before God"--by bringing offerings to the Tabernacle or Temple.

2. High Holidays: 

• The Jewish New Year (Rosh Hashana—“Yom Teru'a” in the Torah), and the
• Day of Atonement (Yom Kippur).

 
Duration
Jewish holidays that were originally one day are now observed as follows:

• Rosh Hashana--2 days.
• Yom Kippur--1 day.
• Shavuot--1 day in Eretz Yisrael or 2 days elsewhere.
• Passover has festival days at the beginning and end of the holiday and intermediary days of lesser holiness, which are called chol ha'moed. In Eretz Yisrael, Passover lasts for 7 days in total and the first and last days are festival days. Outside of Eretz Yisrael, Passover lasts 8 days and has two festival days at the beginning and two at the end.
• Sukkot has festival days at the beginning and at the end and intermediary days of lesser holiness, which are called chol ha'moed. In Eretz Yisrael, Sukkot lasts for 8 days and the first and last days are festival days (the last day is Shimini Atzeret). Outside of Eretz Yisrael, Sukkot lasts for 9 days and the first two days and last days are festival days (the 8th day is Shimini Atzeret and the 9th day is Simchat Torah).

Character
Each holiday contributes its own character to Jewish life (Passover--the theme of freedom; Yom Kippur brings atonement, etc.). 

Celebrating
How to celebrate these holidays is detailed in our Oral Law and halacha books. Jewish festivals as practiced today are similar in holiness to Shabbat. As with Shabbat, the Jewish festival has candle lighting, kiddush at two meals, and havdala.   We eat our best food and wear our best clothing on Jewish festivals (we eat our next-best food and wear our next-best clothing on Shabbat!).
The main idea behind eating meals on Jewish festivals is joy (simcha), so you should drink wine and eat meat (only if you enjoy wine and meat).  There is no third meal on Jewish festivals since people used to eat two meals each day (adding a third meal on Shabbat was for enjoyment/oneg).
 
Melachot
Any activities or actions permitted on Shabbat are also permitted on the Jewish festivals. Actions that are forbidden on Shabbat are generally also forbidden on Jewish festivals, but there are some leniencies (only if the actions are needed for that festival day).
Examples

• Lighting from an existing flame,
• Cooking and baking for the Jewish festival day, and
• Carrying outside the eruv (hotza'a--transferring objects between domains).

 
Grama
Grama (indirectly causing an action) is permitted on Jewish festivals (but not on Shabbat). For example, you may advance or delay a timer that will make a light go on or off in the future (the timer must already be plugged in and operating from before sunset of the festival day).
Note For an action to be considered indirect based on time, there must be at least 2.5 seconds after the first action is done before the resulting action begins to happen.

Psik Reisha Dla Neicha Lei
Psik reisha dla neicha lei is forbidden on Jewish festivals, just as it is on Shabbat.

D'oraita Restrictions
D'oraita restrictions apply world-wide to:

• First and seventh days of Passover,
• First and eighth days of Sukkot,
• First day of Shavuot,
• Yom Kippur,
• First day of Rosh Hashana.

Note The same restrictions apply to all other Jewish festival days but are rabbinical.
 
Women
In general, women are not required to perform the positive, time-dependent commandments. Women and girls are not required to eat any Jewish festival meals except the Passover seder meal (but they are not allowed to fast on those days).

Since two days of Jewish festival are observed outside of Eretz Yisrael, read the lines for the sacrifice for both days that might have been the correct day.

For whether to eat in your sukka on Shmini Atzeret, see Sukka: Shmini Atzeret.
 

Ma'ariv on Shmini Atzeret and on Simchat Torah may be said from 1 1/4 hours before sunset. Kiddush must be said after dark.

Outside Eretz Yisrael, you should eat your meals in the sukka on Shmini Atzeret, but do not make a blessing on the sukka.
 

In Eretz Yisrael, Shmini Atzeret and Simchat Torah are observed on the same day. Outside of Eretz Yisrael, Simchat Torah is the second day of what becomes a two-day festival.

We begin mentioning rain in the second paragraph of the musaf amida of Shmini Atzeret and continue until the first day of Passover.
 
The universal custom is to complete the reading of the Torah and to begin reading it again on Simchat Torah. Dancing and singing with the Torah scrolls is also a universal custom.

Saying the seasonal addition to the amida of mashiv ha'ruach… begins at musaf of Shmini Atzeret. The last time it is said is on the first day of Passover in musaf.

Here are the d'oraita Jewish festivals:

• First day of Sukkot, Passover, and Shavuot
• Seventh day of Passover
• Shmini Atzeret (8^th day of Sukkot)
• Both days of Rosh Hashana.

On these days, you:

• MUST take medicine whenever there is any question of a life-threatening disease or condition.
• MAY take medicine for a condition that affects the entire body (fever, weakness, etc.). Consult a rabbi if possible.
  Exception You may not smear substances on skin UNLESS the fever is life-threatening, in which case even smearing is permitted.
• MAY use some medicines if only part of your body is affected by a non-life-threatening disease--consult a rabbi.

Say she'hecheyanu when lighting candles for:

• Both days of Rosh Hashana,
• Yom Kippur,
• First day (if in Eretz Yisrael) or first two days of Sukkot,
• Shmini Atzeret and Simchat Torah,
• First day (if in Eretz Yisrael) or both days of Shavuot, and
• First day (if in Eretz Yisrael) or first two days of Passover.

Some people have the custom of lighting a yahrzeit candle for a deceased parent on days when yizkor is said: Yom Kippur, last day of Passover; second day of Shavuot; and on Shmini Atzeret.

Yizkor is not required to be said at all, but it is the custom in most places. Yizkor is normally said on Yom Kippur (and the final day of Passover, the second day of Shavuot and on Shmini Atzeret), when many people attend the synagogue prayer services.
Yizkor may be said anytime you wish—even when it is not a Jewish festival--and does not require a minyan.

Begin saying L'David Adonai ori v'yish'i (Psalm 27) on the first day (at night) of Elul, not the first day of Rosh Chodesh Elul (the 30th of Av). The last day to say this Psalm is 22nd of Tishrei (Shmini Atzeret). This Psalm is recited twice daily, in shacharit after shir shel yom and in ma'ariv after alenu, including on Shabbat and Jewish festivals.

Tachanun is related to judgment. Tachanun is NOT said at times of din/judgment:

• At night,
• On Tish'a B'Av,
• In a house of mourning, and
• Yom Kippur.

Tachanun is also NOT said at times of simcha/happiness:

• Shabbat,
• Jewish festivals,
• Rosh Hashana, and
• Rosh Chodesh.

• Isru chag (the day after each of the Jewish festivals),
• Entire month of Nisan.

• All of Chanuka, Purim, Shushan Purim, Tu B'Shvat, Rosh Chodesh, and from Rosh Chodesh Sivan until the day after Shavuot.
• Tishrei from shacharit before Yom Kippur until after Simchat Torah (Shmini Atzeret in Eretz Yisrael). Resume saying tachanun:
  • Second day of Cheshvan, or
  • Day after isru chag of Simchat Torah (this is the more prevalent custom among Ashkenazim). Each person should follow his or her family or community custom.

• Mohel,
• Sandak, or
• Father of a boy having his circumcision.

Jewish Festivals: Medicines: When To Take
Medicine generally may not be used on the d'oraita Jewish festival days.

Jewish Festivals: Medicine for Chronic Diseases
You may take medicine on Jewish festivals (whether d'oraita or d'rabanan) for:

• Chronic diseases, such as Parkinson's disease, or
• Any disease that affects your entire body.

Jewish Festivals: Medicine for Non-Chronic Diseases
You may take medicine on Jewish festivals for non-chronic illnesses, if skipping one day will prevent cure.  You may not take medicine for non-chronic illnesses if skipping a day will just delay your being cured (unless the disease affects your entire body--in which case, you may take the medicine).

Jewish Festivals: Medicines: When To Take: D'Oraita Festival Days
Here are the d'oraita Jewish festivals:

• First day of Sukkot, Passover, and Shavuot
• Seventh day of Passover
• Shmini Atzeret (8^th day of Sukkot)
• Yom Kippur
• Both days of Rosh Hashana (even though the second day is d'rabanan).

On these days, as well as on d'rabanan Jewish festivals, you:

• MUST take medicine whenever there is any question of a life-threatening disease or condition.
• MAY take medicine for a condition that affects the entire body (illness, weakness, etc.). Consult a rabbi if possible.
  ExceptionYou may not smear substances on skin UNLESS the illness is life-threatening, in which case even smearing is permitted.
• MAY use some medicines if only part of your body is affected by a non-life-threatening disease--consult a rabbi.

Jewish Festivals: Medicines: When To Take: D'Rabanan Festival Days
You make take medicines for any reason on d'rabanan Jewish festivals--even medicines not allowed on the first day of Jewish festivals--except:

• Medicines that you smear on skin.
• If the Jewish festival falls on Shabbat (which can only be second day of Shavuot).

To fulfill the two requirements for Jewish festival evening kiddush:

1. Make Kiddush
   Say, or hear, the three Jewish festival evening kiddush blessings/segments:
   1. Borei pri ha'gafen (if on wine or grape juice—preferred option), OR
      Ha'motzi (on two challot if you have no wine or grape juice, since no chamar medina is allowed for Jewish festival evening kiddush; see Jewish Festivals: Kiddush: Challot for Kiddush) AND
   2. Asher bachar banu mi kol am.... mekadeish Yisrael v'hazmanim, AND
   3. She'hecheyanu on all Jewish festival nights, except the last two nights of Passover.  So say she'hecheyanu on:
      • Both nights of Rosh Hashana (in or outside of Eretz Yisrael),
      • First two nights of Passover (1 night in Eretz Yisrael),
      • Both nights of Shavuot (1 night in Eretz Yisrael),
      • First two nights of Sukkot (1 night in Eretz Yisrael), and
      • Nights of Shmini Atzeret and Simchat Torah (same day in Eretz Yisrael).
      Note There is never any requirement on an indvidual to drink kiddush wine (except at the Passover seder), but the kiddush wine must be drunk by one or more persons.
      Note A woman who had said she'hecheyanu when she lit the Jewish festival candles does NOT say she'hecheyanu again if she makes kiddush for herself, even when making kiddush at the Passover seder.
      Note There is no need to eat a new fruit after saying she'hecheyanu on the second night of  Shavuot, Passover, or Sukkot. This is not comparable to Rosh Hashana, since the second festival night was instituted due to uncertainty of the actual date of the holiday, while Rosh Hashana is considered to be one single, long day.
2. Establish a halachic “meal” (kovei'a se'uda).
   For how to establish a halachic meal, see Introduction to Jewish Festival “Eating a Meal” Requirements.