sometimes I draw chin first without any consent of how the upper part of the face will turn out, but I only do those when Im lazy or just bored, but when Im determined to make a good artwork, I start with a circle and draw figures first, although I can only do it on pencil and paper.
It is longer in reality; first the idea in my head is born and then to sketch in paper or in MSpaint. After I am happy with the sketch I make the lineart and clean the lines and end with photoshop.
It begins with the imminent circle which I use to build from, depending on the positioning and stance of the character then I use this circle for a different parts of the body, making my judgement accordingly. If the character is clothed plumply, which is a preferred means of design for me, then it's easier to map out the key components of the character's stance due to anatomy being then only partially involved. I find this technique makes a particularly nice go at cartoons. This abstraction from reality or anatomy how it is known best is also what I favor a lot in my drawings. So I don't particularly mind about the skewing and distortions that come with putting clothing high up on my priority list before mapping out anatomy. Whatever works though, really.
By the way, don't be disheartened by those who patronize you about drawing anime, most are condescending comments that aren't worth reading. There is an abundance of anime on-site and admittedly, I like to deviate from drawing it a lot these days to something more expressive (for me) being cartoon - but anime should be more accepted than what it is. A fun fact is that I have a lot to thank anime and other types of Japanese art because it's what I was influenced by most during my early years. It sort of shows beyond that of the actual anime pieces in my portfolio, where there is bold outline with flat colour in-between.
Takashi Murakami is respected in his field and his movement: Superflat. It's a contemporary art influenced heavily by anime and otaku culture - check 'em out! <3
Do you just sketch and color it?
Basically, how do you draw anime (or anime-like) characters?