Help with quotation marks and punctuation please?

I'm writing an essay for a school project, but I'm a little confused about how to correctly punctuate it. It's a competition, so I don't want to get marked off for incorrect punctuation. Let's say this is what I'm quoting:

Andreas Vesalius was an influential person in the history of anatomy.

Would I put the punctuation in the quotations:

"Andreas Vesalius was an influential person in the history of anatomy."

Or outside:

"Andreas Vesalius was an influential person in the history of anatomy".

Also, what if I was to continue writing after the quotes?

"Andreas Vesalius was an influential person in the history of anatomy," says professor Something-Something.

I am also using footnotes, if that makes any difference.