The term "DIRECTOR OF PHOTOGRAPHY" is exactly what it says on the tin.
You are the expert on photography.
Yes, go and take photographs, explore, experience, read, watch as much as you can. Get tech references on films and then watch them. Pause it in a shot and really study what you are seeing.
Ask yourself, what was the DP trying to achieve?
In the meantime whilst you are 'studying', get on set and work the different roles in the camera dept, earn your stripes!! It will not only teach you about the timing and flow of a crew on set but it will also show you what you are naturally good at and need working on.
Hope this helps and good luck!
S