I would start off looking at characters that I like, then copy them
put paper on top of them and copy the original with pencil, then outline it with ink (a thin fine tipped sharpie or india pen) Erase pencil after you draw in sharp pen lines*
Practice rendering it EXACTLY how they achieve whatever aspect you're looking for, say how they show shine on hair/eyes, how they make muscles bulge etc.
That I know of, lots of anime artists use illustration markers, available at Blick or art stores, or they use Prismacolor markers.
This isn't the creative step, but if you can achieve the same looks pros. use, you can apply the same techniques to your own art
Then I would go to Deviantart.com and look at people's anime (influences) and gather my own ideas for a character, then I would draw him/her in just in lines (with a fine tip), THEN copy my lined drawing with a scanner. That way if and most likely you will mess up on your first attempt, you can still work with the exact drawing, keep doing it until I'm satisfied with it's look. Then finally practice drawing emotions, reactions, action sequences.
It wouldn't hurt to look at youtube to see how people apply marker work. In general, usually but not always, you put the lighter colors first, followed by darker.
Good luck!