In the grammar translation method language is taught by translating texts and studying grammar. There is little or no place for the spoken language. This method is what many of us will remember from school.
The direct method involves using only English in the classroom. A typical beginner lesson would include showing objects to students, telling them what they are called in English, getting them to repeat. This language is then built up to sentence level, eg “this is a pen” and then to questions eg “What is this? Is it a chair?”
The audio-lingual method is based on behaviourist learning techniques. Students listen to a structure and repeat it. When the teacher thinks it appropriate (s)he starts drilling the structure.
E.g. teacher: “He” students “he’s playing tennis”
“They” “they’re playing tennis”
“Question” “are they playing tennis?”
The objective of the audio-lingual method is to help students produce the language automatically.
The notional or functional syllabus takes a different approach. Language is studied according to the usage. The syllabus is structured according to the function or use of the language. For example, elements of the syllabus could be ordering food in a restaurant, making an appointment, asking for and giving directions. At one time this was a popular method for teaching business English.
The communicative approach involves creating a real need for communication. Typical activities include role plays, information gaps but this approach is not confined to speaking activities. For a more detailed description, you can see my reply to Joselyn in April.
Task-based learning involves giving students an activity or a problem to solve. The teacher notes down mistakes that students make and this guides decision-making for language areas to work on.
An eclectic approach is where a teacher makes use of techniques from the various methods and applies them when appropriate. This will depend on the focus of the lesson and students’ preferred learning styles.
This is a very brief overview of some methods for teaching. It is in no way complete and space does not allow me to go into the methods in detail. If you are interested in knowing more, there are many books available and you could always write in with more questions.