Many institutions use something they call "Harvard" reference style. Harvard referencing is an author-date style often used in medicine studies. However, Harvard reference style is not a defined style. Rather, it is a generic description of any author-date reference style. All of the following could be Harvard style (I= initial of author's first name):
(Author I, date)
(Author I date)
So, you see, for the in-text references, several different formats are possible, depending on whether the style includes the author's first initial and whether there is a comma separating it from the date. Things get more complicated when you add a page number for the reference; this could be separated with a comma, a colon, or the letter p (with or without a period).
There are even more variations for how the references section is organized in the generic style known as Harvard. Although APA is very clear about how to write a reference list, a Harvard style reference list can vary a lot. I've seen them where the author's names are all capitals, with or without first names written out, or using italics in different places.
So what are you to do if you are using Harvard as a reference style? Don't go looking to Harvard University to answer your questions. It is not the official style of Harvard University. In fact, Harvard style is most often used by universities in the United Kingdom and Australia. American universities tend to use APA for humanities and business papers. Canadian universities often use Vancouver Style for medical writing.
Since Harvard is a generic system, you need to find the details of the style in order to be able to use it. What Harvard style means is that you should check with your institution's library for details of your university's version of the Harvard style of referencing. It's a little misleading to simply tell students to use a Harvard system, it would be more accurate to tell students that the institution uses an author-date style and to get details from the library.
Harvard style is often used in medicine. The other main medical citation system is Vancouver Style. Vancouver referencing uses a numbering system for in-text references. Beginnning with 1, the Vancouver Style numbers references in the order that they are cited in the paper as a superscript. The reference list provides details of the citations in the same order. Details on how to write the reference list can be found here.