What do Jews do to show their faith every day?

Answer 1

By keeping all the hundreds of mitzvoth (commands), principles and beliefs of the Torah. Though it may have an associated culture and one or more associated languages, the traditional definition of Judaism is the observance of the Torah, which is why dictionaries define Judaism as "the religion of Moses." In this sense, the word "Torah" is meant in its wider meaning, which includes the Tanakh, the Talmud, and other classical Jewish texts.
The philosophy of Judaism is that this world is a purposeful creation by God, in which all people are tested concerning their use of free-will. We possess a soul which lives on after the body dies and is held responsible for the person's actions.
Some examples of the commands:

• Putting on Tefillin (phylacteries) in the morning (Deuteronomy 6)

• Saying the Shema-prayer, stating that God is One (Deuteronomy 6:4)

• Keeping kosher (Deuteronomy 14)

• Paying workers on time
  
• Marital rights for one's wife
• The Ten Commandments

• Helping someone who is in danger
• Returning lost objects when feasible (Deuteronomy 22)
  
• Wearing the tzitzith-garment (Numbers ch.15)

• Affixing a mezuzah (small parchment scroll) to the door (Deuteronomy 6)

• Learning Torah

• Keeping our rules of ethics

• Marrying and having children
  
• Educating one's children in Judaism
  
• Giving tzedakah (charity)
  
• Honoring one's parents
  

And many more.
The laws have various reasons. Some (such as the Passover) serve to reenact or remember events of our history.
Some (such as saying the Shema-prayer) serve to reiterate our belief in God.
Some of the laws (such as those of ritual purity and kosher food) serve to sanctify us.
Some (such as the laws of torts) serve to maintain an orderly and just society.
Some (such as the law against breaking a vow) serve to prevent bad character traits.
Some (such as the command to offer help) serve to engender good character traits.
And all of the commands serve to subjugate us to God's will (especially those commands for which no explanation is easily apparent).
Note that the Torah "as is" isn't exactly what Judaism observes. Rather, it's the Torah together with the details provided in the Talmud, which is the Oral Law that was handed down together with the laws of Moses. Otherwise, the verses of the Torah often lack enough detail to be fulfilled as is.

Answer 2

Religious Jews live by the Torah, by obeying its commands and beliefs.Link: Jewish beliefs
Some examples of the commands:

• Putting on Tefillin (phylacteries) in the morning
  

Link: The Tefillin

• Saying the Shema-prayer

Link: The Shema

• Keeping kosher
  

Link: Kosher-laws

• Paying workers on time
  
• Marital rights for one's wife
• The Ten Commandments

Link: The Ten Commandments

• Helping someone who is in danger
• Returning lost objects when feasible
  
• Wearing the tzitzith-garment
  

Link: What are Tzitzith

• Affixing a mezuzah to the door
  

Link: What is a mezuzah

• Learning Torah
  

Link: The Torah

• Keeping our rules of ethics

Link: Jewish ethics

• Marrying and having children
  
• Educating one's children in Judaism
  
• Giving tzedakah (charity)
  
• Honoring one's parents
  

And many more.

See also the other Related Links.

Link: What are the teachings, practices, principles and beliefs of Judaism?

Link: What is life like for Jews?

Link: More about the Hebrew Bible

Link: More about the Talmud