How do I properly reference?
The Harvard citation system does not use reference numbers.  It uses, as you describe, the author's last name and publication year.  (This is similar to the APA citation style.)

The reference lists should be at the end of the document, not listed as footnotes.  So your understanding of the Harvard style seems to be basically correct.  Some more details about the Harvard citation style are given here: http://www.citethisforme.com/harvard-referencing 

Personally, I too prefer referencing by number rather than author, but if you are supposed to use the Harvard style, then you just have to use it.