How do I edit the storage on my iCloud AND back up my iPhone with a broken screen?

I dropped my phone and the screen faded to black. Now when I press the home button it lights up blue/navy, but does not respond to touch. I still get notification sounds/vibrations, but I can not see my screen or unlock my phone at the moment.

I was wondering if there was any way to save my pictures and other files on my phone? Do I just need to replace the screen? Can I do that at the Apple Store or with AT&T? Is there a way to edit and back things up with my macbook?