How is Judaism practiced?

Answer 1

By obeying it. Orthodox Jews believe that the Torah must be fully observed. Other Jewish groups (Conservative, Reform) adapt, curtail or change the Torah-laws in contemporary life, to a greater or lesser degree.

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

• Sitting in the sukkah during Sukkot
  

Link: The Sukkah-booth

• Avoiding leavened products in Passover
  

Link: Passover

• Keeping kosher
  

Link: Kosher-laws

• Not eating on Yom Kippur
  

Link: Yom Kippur

• Not working on the Shabbat
  

Link: The Shabbat

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

Link: The Ten Commandments

• Helping someone who is in danger
  
• Counting the days of the Omer
  
• 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.

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.

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