Anime/manga can be very hard to draw, as you're usually trying to copy some one elses style of drawing, which can in some instances, halt you progressing in creating your own style of art, which means you can only improve so far.
By all means, find some an artist's who's style you like, and progress from there, don't try and copy them exact.
Devianart has a number of tutorials to help draw the atypical anime style.
I wouldn't advise on those books you can get from art and book stores. I baught one from a school book club a few years ago, and was so disappointed to find that the art style in the book was actually considerably worse than my own.
Each person has their own strengths. I'm actually quite good at drawing faces, hair, hands and feet, but everything else in between tends to fail. I've only actually learnt how to draw folds in clothing since going to art school, and even then it's something I need to improve on.
Do some sample drawings, and ask people (nice people, friends, family) what they honestly think you're good at drawing, and what you think you need to improve on, and concentrate, but not soley, on practising drawing them.
You're own wrost critic sometimes, but this only means that you strive to improve yourself further, and one day, when you finally release a piece of art to the public, they're fascinated by it, despite the fact you've taken so long and probably hate the piece by now.
I'm not saying you're not allowed to actually like your work, but always look for things to improve on.
In other words. Practise Practise Practise...With references, but don't copy.
Hope this helps, if not...Sorry
