I primarily use the communicative approach, which focuses on interaction, communication and fluency over memorization. You will still learn plenty of vocabulary and grammar, but you will learn it in context as you learn how to truly communicate. You will learn to understand and be understood. We will learn to speak, read, write and listen, the four ‘skills’ of language learning.
The most common teaching methodology is Audiolingualism, which is seen in language CDs, books and most classes, and involves memorization and repetition. Audiolingualism is boring, inefficient and ineffective. You do not learn to communicate in any meaningful way, and are unable to respond to new vocabulary and situations that you haven’t already memorized and rehearsed. I do integrate some Audiolingualism in my curricula for older students and children, who benefit more from repetition, but I use it in conjunction with other teaching styles and never rely on it exclusively.