A Torah scholar should stand up for another Torah scholar who is greater in knowledge; a greater Torah scholar should acknowledge the lesser scholar by standing up a little bit.
 

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).

WERE BOTH FOODS LESS THAN 120° F?
YES

ARE BOTH FOODS SOLID?
YES
Status If you can separate them (there are no cracks in the meat), both foods are kosher.  Consult a rabbi.
What to Do

• If one or both of the foods were already cooked, separate them and wash with soap and water (if possible).
• If it is not possible to separate them, just cut off the thinnest slice possible from each surface of each food which had been in contact with the opposite gender food and you may use the food.

NO
SOLID FOOD FALLS INTO LIQUID FOOD OR LIQUID FOOD FALLS ONTO SOLID FOOD
Status If both foods are cold and you can separate them (there are no cracks in the meat), they MAY be kosher.  Consult a rabbi.
 

• Both foods are non-kosher if they cannot be separated.
• If you can separate them enough that one becomes less than 1/60th the volume of the other:
  • The larger food is kosher.
  • The lesser one is non-kosher. 

What To Do

• Once the two foods are separated, wash or otherwise remove the smaller food from the larger one.
• If not possible, cut off the thinnest slice possible and you may eat the remaining food.

Note If there are cracks in raw or cooked meat, and if you can clean off enough of the dairy spill so that the remainder is less than 1/60th, it may be kosher--ask a rabbi.
 
LIQUID FOOD FALLS INTO LIQUID FOOD
Status Both liquid foods are non-kosher.
Exception If one liquid food is less than 1/60th the volume of the other one, the mixture is kosher.
Note If non-kosher wine is involved, see below.
 
SOLID FOODS, ONE OR BOTH ARE HOT
Status If one (or both) of the foods is hotter than 120° F, both foods are non-kosher.
Exception If one food is less than 1/60th of the volume of the other:

• The larger-volume food may be kosher (consult a rabbi).
• The smaller-volume food remains not kosher.

Possible Exception  If the food on the bottom is cold and thick, consult a rabbi.

If either food is spicy, see above.
If any combination (solid and liquid; solid and solid which are in any liquid; or liquid and liquid) of dairy and meat were soaked together for 24 hours or more, even if cold, they are all not kosher.
Exception In any of these three cases, in which one is less than 1/60th the volume of the other:

• The larger food is kosher.
• The lesser one is non-kosher.

Note You must remove the smaller food from the larger one and wash off the larger one, if possible. If you don't know how long the foods soaked together but it may have been less than 24 hours, you may use the foods.