Drawing anime, or Japanese animation, relies on the same fundamental concepts as drawing Western cartoons or realistic figure drawing, such as proportion, perspective and shading. Because anime is an umbrella term, there is no single style to learn how to draw. However, studying reference materials is helpful to develop style.
First, it helps to purchase figure drawing and artist-centric anatomy books as references to learn basic figure-drawing skills including the line of action, the pipe construction and other figure-drawing techniques. One of the most well-known and comprehensive books is "An Atlas of Human Anatomy for the Artist" by Robert Peck.
Getting pencils and paper and practicing each day helps to build skill and muscle memory in the hands. Although sophisticated pens and paper exist specifically for drawing manga, or Japanese comics, the beginner should use basic tools when starting out.
Once the beginner feels comfortable with the basics of human anatomy, she can work on stylizing her drawings. Whether she wants a more rounded art style like that of Rumiko Takahashi of "Ranma 1/2" and "Inuyasha" fame or a hard, angular "Dragonball Z" influence, plenty of anime and manga exist as reference guides. It's helpful to practice drawing these characters in alternate poses based on your knowledge of how anatomy is put together.