How did religion influence the culture of the Israelites?

Answer 1

Hebrew society (the society in ancient Israel) was based upon the covenant with God, as set forth in the Torah. There was always a learned class among the Israelites, and virtually all men and boys (and a good percentage of women) could read and write. A portion of each day was spent praying, and another, larger part of the day, was spent studying Torah (by a good part of the populace). Religious questions (and torts) were brought to one of the many Rabbis or Jewish courts. Having a large family was an ideal, as was welcoming guests into the home, giving charity, and other forms of kindness. A portion of crops were given to the poor. The calendar year was replete with the Sabbaths and festivals; and blessings were said before and after eating and on many other occasions.
In brief, there was no such thing as a secular part of life, since the Torah's laws cover every form of activity, including business.

Answer 2

The Hebrew Bible reiterated the teachings of Abraham (Talmud, Yoma 28b) and codified their exact details; and at Mount Sinai, the Hebrews (the Israelites) accepted as obligatory what had until then been national custom. The Torah and Prophets shaped our ways of thinking and provided a national legal code.Link: More about Abraham

• Practicing kindness and avoiding dishonesty became obligatory instead of merely proper.
  

Link: Israelite ethics

• Agriculture in the Holy Land included tithes to be given to the Levites and Kohens, thus providing for a scholarly class of people. One of the tithes was given to the poor, thus obviating the existence of starvation.
  
• Immorality and incest were legislated against in detail. Instead of instinct or "crimes against nature," they were subsumed into religious law.

• The roles of king, prophet, Kohen, Levite, officers and judges were all provided for in the Torah, thus defining the shape of the society and its institutions and providing certain balances.

Link: King, prophet, Kohen, officers

• The Israelite year was filled out with the Sabbaths and national festivals; and they were imbued with the function of worshiping God instead of being secular celebrations.

Link: Israelite festivals

• The judges were commanded to fear God (Exodus 18, Deuteronomy 1), instead of relying on their skills of jurisprudence alone.

• The laws of the Tabernacle (and later the Holy Temple), and commands to love God and fulfill all of the commandments, were written in the Torah together with (and mixed among) the seemingly mundane laws of restitution, testimony and witnesses (etc.), in order to convey the message that for us it is all part of religion. Secular life was a foreign concept. For example, a shopkeeper would be constantly aware of the religious laws of maintaining honest scales, giving a tithe to the poor (maaser kesafim), not overcharging, returning lost objects left behind, etc.; and he would set aside times for the daily prayers.
  

The above are just a few examples.

Hebrew (Israelite) society wasn't perfect. We are human; and as seen in the Prophets, there were times of backsliding and various pitfalls. But to the extent that the people kept their national laws and tradition, the society was exemplary and created a model which has influenced the Western world down to today.

See also the other Related Links.

Link: How did the Israelites influence modern society

Link: How do our Jewish beliefs affect us?

Link: Jewish life in Israel