I think that reading the manual and playing/trying everything is a good way to learn. I think it worked for me Reading the manual allows you to have a look at all the features the camera has, and playing gets you used to using it
Play around with the settings as you read from manual. You will learn to use all functions in no time. If you find yourself taking picture with good exposure and no handshake, to me it means you already got the basic foundation. There are more to learn as said photography needs life long learning.
I agree that "mastering the photography eye" is important, but what's the point if you can't get your tools to do what you want? It's important to learn the camera and how to use it so that when you are getting the shot you want, you won't be stuck thinking about how to make it do what you want, you can concentrate more on the image.