I haven't worked alot with cutting out things from detailed pictures, like photos. In this case I have a picture of Charles Darwin, I want to cut out his head and I was wondering what the best techniques for that task would be the best for removing his head.

If you want to do it roughly, IE: in the shape of a circle, then you can use Inkscape's clipping function.

If you want to essentialy remove the background, then Inkscape is not the best tool to use. I recommend the gimp, an open source (free) photo editor akin to Photoshop. This tutorial explains how to extract a background using the gimp.