The Torah service traditionally takes place three times a week: on Monday, Thursday, and Saturday (Shabbat) mornings. We also read from the Torah on some holidays, and some communities hold Torah services at other times -- like Friday nights -- as local tradition.
The Torah service imitates the Revelation of the Torah on Mount Sinai: the Procession/Hakafah presents the Torah to the community with great fanfare, and the Reading/K'riyah reveals a portion of God's Torah (and sometimes, also a Prophets' words/Haftarah) to the People of Israel. The blessings before and after the readings praise God for choosing the People of Israel as the recipients of the Torah's wisdom.
Some communities also say a prayer for healing while the Torah is out: