I had the same issue very recently. But in my case I went down the semi realism path because I wanted my style to have influences of realism, I hate pointy chins and huge bug eyes. All I could really say is look at series which have an art style you want to emulate. It might take a little bit to get back into the flow of anime but you'll get there soon enough, don't worry.
Oh my, well, i havnt actually found my own art style (I wind up drawing fan-art most of the time and i try to stick to that particular style while drawing fan art) so drawing precise 'anime' style is difficult. As there's the awkwardly pointy style that would generalized in Cowboy Bebop (though its a mixture of pointy and round, dem pointy chins) and i suppose Panty and Stocking is the best example for Rounded, since almost everything there is round. I guess the best way to get back into the 'style' is to pick an anime whose style you like, look at one of the characters, and simply draw the face shapes. and eyes? Pffft there are like a gazillion different eyes you can draw for anime. Eyes the size of dinner plates, just black dots, manly with eyelashes, round, sharp, wide, small, boxy, triangles. Eyes are for you to decide.
Japanese cartoons, exactly. The art of cartooning is a global thing. You deliberatively simplify details for a desired effect. The differences are regional but not as rigid or as insular as you might think.
Tracing is tracing, trying to reproduce a image to figure out it's style is like when you draw off a model to try to figure out how to draw the human form. I'm not saying trace it, because that does you no good. Just have the image next to you and try to reproduce it. It's the best quickest way to pick up the components to a specific style, and once you pick those up, you can apply them to your own pieces.
No matter which Cartoon Style, its all about constructing the basic forums of the human body. There are many anime styles. The only way is to look at your favorite anime styles and then study them, and break em down into simple shapes as you would in realism, semi realism, etc. Use anatomy and all those as a guide to help you with the human body.
All forms of cartoons are just exaggerations of the human body, made to be more expressive. For anime, most of the exaggeration happens in the eyes. The bigger the eyes, the younger and innocent the person looks. Also by lowing the eyes, makes the person younger (simular to chibi styles). The more normal the eyes, the older you look, and smaller makes you more mature.
Its kind of like having giant baby eyes with an adult body.
Why do I say there is different styles? Because anime in japan is just animation. The eyes do not make the animation, just having something that is animating/moving on a screen drawn, or rendered in 3D, is anime to them. Also that there is just some few animations of anime that don't have a pointy chin or nose, or consistent height, etc.