Downloading images from posts

Hi guys.

I’ve recently got into web development, and until now it was pretty much a fun ride where I could just figure out the solution to every problem I encountered personally. A few days ago I started a new website using the Twenty Twelve theme, on which I post only images. I figured out it would be a good thing for a user to be able to download the full-sized image with a single click, so I wanted to add a download button at the end of each post. I know there are plugins to add download buttons, but they require that you add the download link to each post manually. My goal is to make the system more automatized, in a similar fashion of the Facebook like button which appears on the each page automatically.

For past two days I searched for a solution for my problem but haven’t been able to find one. As i final resort i decided to join this community and seek for a help. Is it possible to achieve this with a simple method?
I figured out how to make a button and style it, but I don’t know what to point it to in order to download the image from the post.

Also, my website is not live so I’m not able to provide a direct link. I’ll post the screenshot If needed.