Prescriptive approaches to language teaching include methods such as audio-lingual. A prescriptive approach describes how the teacher should conduct the lesson and how the students are expected to respond.
If you take a look at the Streamline series of books, you'll see what I mean. The teacher's handbook outlines in detail how the teacher should handle each segment of the course. From memory, I think it also gives examples of student responses. Such methods are intended to give the teacher very little scope for improvising or creativity. The same goes for the students. The audio-lingual method includes a lot of drilling and repitition. Errors are drilled until the correct response is produced automatically.
Descriptive approaches, on the other hand, put students at the centre of the learning process. The learner (a term prefered over student) is seen as a whole person and is treated as an individual. Learners are encouraged to express opinions and they engage in communicative activities. They are also encouraged to experiment with the language; risk-taking is seen positively. Errors are also seen in a positive light as they provide an opportunity for learning.
Both approaches have advantages and disadvantages. As a teacher, your task is to choose a method that suits your teaching style and the learning style of your students. Many teachers have a style that incorporates techniques from the various approaches.
Many volumes have been written on the different methodologies. This is an overview of them. As you are starting out teaching, I don't think you need to worry too much about the finer points of the distinctions. Just enjoy your teaching and try out different methods. As a taster of the descriptive approach, you can look at books by Mario Rinvolucri or "In Your Hands" by Jane Revell and Susan Norman.