The Hebrew word kana means "subdue" or "bring low", and is the scriptural word for either subduing an enemy in combat or subduing your own soul in actions of humility. (This word is a homonym of the word that means "jealousy". They are spelled very differently.)
Another Hebrew word, tzoom, literally means closing and more explicitly refers to fasting. But it is the word kana which provides insights into the concept of fasting.
In the Tenach we read of many nations being subdued in whole or in part: Moav (Judges 3:30), Canaan (Judges 4:23, Nehemiah 9:24), Midian (Judges 8:28), Ammon (Judges 11:33), the Philistines (First Samuel 7:13, Second Samuel 8:1), the northern kingdom of Israel (Second Chronicles 13:18), and the southern kingdom of Judah (Second Chronicles 28:19).
God also prefers that repentance be visibly accompanied by a subdued heart (Leviticus 26:41, Second Chronicles 7:14, 12:6-7,12). Ahav demonstrated subduing himself by tearing his clothes, wearing sackcloth, fasting, and walking softly (First Kings 21:27-29). Josiah demonstrated subduing himself by tearing his clothes and weeping (Second Kings 22:11,19).
In the Psalms we first read of a link between having anah, an attitude of humility, and the actions of kana, such as fasting (Psalm 35:13). Later on Isaiah and Ezra also write about people trying to nurture anah with fasting, sackcloth, and ashes (Isaiah 58:5, Ezra 8:21, Nehemiah 9:1). Not only do people view fasting as part of demonstrating humility and repentance but God also connects fasting with repentance (Joel 2:12).
Fasting was done by people praying petitions to God (Acts 10:30). Yeshua agreed that fasting can somehow make our prayers more effective (Matthew 17:21).
People also fasted when appointing others to leadership (Acts 14:23).
By the first century, Jewish culture had solidified the link betwen the concepts of anah and kana. Fasting, wearing sackcloth, and walking softly were the three standard ways to cultivate a constant attidue of humility, to "afflict your soul" on Yom Kippur, or to participate in the oath of Numbers 30:13.
Other behaviors latter written about in the Talmud may also have been understood as part of kana as early as the first century. These include sitting on low seats, abstaining from bathing or haircuts, and abstaining from sexual activity.
Fasting twice a week was an established first century practice (Luke 18:12).
The Didache gave advice about this twice-weekly fasting to the early followers of Yeshua:
"let not your fastings be with the hypocrites, for they fast on the second and the fifth day of the week; but you keep your fast on the fourth and on the preparation day [sixth day]."
To the best of our congregation's knowledge, scholars are unsure if this twice-weekly fasting was of one meal or all the day's meals, and no longer know the context of the argument about which days to fast.
According to Talmud, on minor fast days people are only expected to fast from sunrise (after an early breakfast) to sunset (when they day ends). This reference is from a later century, but potentially describes practice of skipping two meals that was present as far back as the first century.
We who follow Yeshua must also subdue ourselves.
Yeshua told his followers they would fast after he left them (Matthew 9:15) and taught about how to fast (Matthew 6:16-18) but not how often.
Fasting is still important for character development, prayer, and humility.
Even though humility is a type of focus we should always have, there are days that scripture mentions as appropriate for special devotion to humility, fasting, and prayer. These are appropriate occasions to study, discuss, and grow in humility, as well as occasions to focus on God for hours at a time without interruptions.
As mentioned above, fasting twice each week (probably skipping one or two meals each fast) was an established practice in the first century. This may or may not be an appropriate practice for Yeshua's followers today, depending upon other aspects of their schedule and responsibilities.
Yom Kippur is an appointed time that scripture asks the Jewish people to "anah their souls". Traditionally this is done by fasting and abstaining from pleasures. Yesuha's followers can also benefit from setting aside this appointed time for reflection, repentance, and fasting.
Zechariah 8:19 mentions four fast days that commemorate tradgedies related to the start of the Babylonian Exile.
These four days, although not required as fast days in scripture, are appropriate days to fast and pray for Israel's protection.
Rabbinic culture has established two other fast days which may also be appropriate times for some of Yeshua's followers to pray and fast.