Do what I tell alot of new people here. Put your camera in Av Mode and leave it there for 100 shots. During those 100 shots fool with the ISO, f-stop. Under no circumstances shoot in any of the auto modes.
Av still is an auto mode, really. Everything but M is some sort of auto mode. And then if you're just shooting using your camera's light meter, then you might as well be using some sort of automatic mode anyway.
IMO, you can't just say you want to "learn;" you have to decide what you want to learn.
If you want to learn how your camera operates, read the manual and mess with your camera. Worse you can do is be forced to revert to factory settings. If you want to learn the relationship between ISO, shutter speed, and aperture, read about exposure. Take some pictures specifically experimenting with depth-of-field, motion blur, bracketing, etc.
Learning about composition, though, is a whole other matter. It involves both study of the subject through reading and looking at other photographers' work, as well as taking a lot of pictures on your own, being conscious of objects within the frame, lighting, color contrasts, textures, etc. And, of course, subjecting yourself to criticism.