What do Jews do for their religion?

Religious Jews live by the laws of the Torah, by obeying their commands. There are hundreds of examples.
The laws themselves 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 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).
A few of the commands are:
Putting on Tefillin (a.k.a. phylacteries) in the morning
The sukkah-booth during Sukkot
Avoiding leavened products in Passover
Not eating on Yom Kippur
Not working on Saturday (Sabbath)
Paying workers on time
Marital rights for one's wife
Counting the days of the Omer
Returning lost objects when feasible
Wearing the tzitzith-garment
Learning Torah
Marrying and having children
Educating one's children in Judaism
Giving tzedakah (charity)
Honoring one's parents
And many more. Note that the Mosaic law "as is" isn't exactly what Judaism observes. Rather, It's the Mosaic law together with the details provided in the Talmud, which is the Oral Law that was handed down together with the laws of Moses (the Torah). Otherwise, the verses of the Torah are often too brief (lacking detail) to be fulfilled as is.

Within the religion of Judaism, there are many different practices and holidays that are followed and celebrated. They have a celebration for the new year, and they attend services on Saturdays.