Here I am going to explain the main ideas of some methods:
The Audiolingual Method: it is mainly focused on oral activities, in where the development of pronunciation is very important. This is made by conversations, repetitions and pattern drills. Grammatical explanation is not important.
The Community Language Learning: it is based on the affectiveness between the teacher and the students. The learning methodology consists on the teacher translation of the learner's ideas, and the post repetition of those ones by the learner. The effectiveness of the method relies on the translation capacity of the teacher.
Suggestopedia: it is method that states that the learning process is successful when the learner is relaxed and feels comfortable. For this, music plays an important role in the learning process.
The Silent Way: it promotes that the learner has to create meaning through the manipulation of physical objects and the resolution of problems. The teacher is in silence most of the time, but guides the students to the solution.
Total Physical Response: students learn carrying out comands given by the teacher. They listen to the instructions and they do the actions.
The Natural Approach: in this method, the students received comprehensible input for a period of time and they don't say anything. Later, they are able to produce and to communicate in the language.