No you are not crazy. Microsoft has made this functionality non-trivial enough that it is unfortunately worthy of a blog post. This is for me and the next time I forget how to do this.

Go to your SharePoint sight and click ‘SharedDocuments’


Then ‘Library’


That that little explorer folder icon with a computer


A explore window should pop up allowing you to drag and drag files into directories.
You may also want to get a coffee at this point because dragging a single file takes about 10 years to complete so make sure you have lots of time.