How to study Judaism?

Answer 1

Pirke Avot (the Ethics of the Fathers) says, find yourself a teacher, and that advice remains good. The best way is to study with a rabbi. Many rabbis offer introduction to Judaism courses. These are frequently seen as courses for potential converts, but taking such a course does not commit a person to conversion.

Short of that, there are lots of good introductory textbooks. I personally enjoy Telushkin's encyclopedic works, Jewish Literacy and Jewish Values. Kertzer's What is a Jew has remained in print for well over 50 years (it's much smaller than Telushkin's works). Steinberg's Basic Judaism is a tiny little book, but for many people, a small bite is a good way to begin.

Answer 2

Most synagogues support 3 kinds of talmud Torah (Torah study):

-- as a component of the service. Most siddurim (prayerbooks) contain selections of study passages and, when the service reaches the point where those passages are, the service leader may instead refer people to other material (Bibles, other parts of the siddur) for a study session.

-- as a component of classes outside the service. Most synagogues offer religious school instruction for children and adult-ed opportunities for others in the congregation. Classes in preparation for conversion, Talmud classes, classes on Mussar (Jewish ethics) and more. Much of the content of these classes is directed study and discussion. One characteristic of such study is pilpul, a style of analytical argument that can become quite technical.

-- private study. Synagogues usually have libraries with a wide range of books. People are welcome to use these libraries for personal undirected study.