Over the years, the study of Latin has become associated with the endless rote memorization of noun declensions and verb conjugations. However, are other approaches to the study of the language and different textbooks reflect different methods. This is a very brief overview.
The Reading Method
The Reading Method is a very popular and effective way to learn Latin. Students learn Latin by reading carefully written stories that gradually build up from simple sample sentences to complex selections. Students learn to develop their reading skills through metaphrasing and grammatical expectation. The focus is upon building reading fluency through extensive reading. Grammar is important but the focus is upon the purposeful use of that grammar toward the end of reading a classical text in its original language.
Popular Reading Method courses include the Oxford Latin Course, the Cambridge Latin Course, and the Ecce Latin Course.
The Direct Method
Proponents of the Direct Method believe that Latin should be understood as a language, not a complex code. The Direct Method is an immersion method. It is sometimes called the Nature Method. Students learn Latin in Latin without the interference of their native language. Grammar is taught in the target language. Speaking, listening, writing and reading (not translating) Latin are important components of the Direct Method.
The most popular and readily available Direct Method course is Hans Oerberg's Lingua Latina Per Se Illustrata, which has become very popular in the United States. Piper Salve is a popular Direct Method Latin course published in Germany. Principia and Pseudolus Noster are part of a two part British series, now out of print.
The Grammar Translation Method
Still, many consider the study of Latin Grammar to be the most important focus of learning a Classical language. The Grammar-Translation method gives grammar the center stage and translation has a supporting role. Students learn declensions and conjugation, paradigms and syntax and apply that knowledge toward the translation of Latin texts into the English language. In a very formal Grammar-Translation course, forms are taught first and only simple syntax. After students have mastered the declensions, conjugations and other morphological paradigms, they then begin to examine syntax more closely. The ability to translate from Latin to idiomatic English is the goal of the Grammar-Translation method. For some very conservative proponents of the Grammar-Translation method, the ultimate goal is a better understanding of the English language. Most Grammar-Translation teachers, however, have the ultimate goal of learning to read and translate Latin with precision and accuracy.
The most famous Grammar-Translation textbook is Wheelock's Latin. Other well-known Grammar-Translation series are Jenney's Latin and Latin for Americans. These three textbooks have been used by Latin students for decades.
A more recent Grammar-Translation textbook is John Traupman's Lingua Latina (not to be confused with Oerberg's Direct Method textbook by the same name.) Galore Park's Latin Prep and So You Really Want to Learn Latin are increasingly becoming popular as well.