In my experience, It's pretty difficult, as you need to be able to
base64encode the file before it's sent to the server (this can accomplish in some browsers Firefox, Chrome, Safari? Probably not IE.)
Also, to get VisualForce to properly encode the 'form-data' that is being submitted to the server you need to create a VF form that points directly to a 'File Input' field, which is hard to link to a drag and drop functionality. So I recommend doing something like:
<iframe src="myvfpage_with_file_input_form" style="display:none; />
And have your parent page fill in and submit the form on the hidden vf page in the form when the drag and drop takes place.