Where do you put the period in a quote?

If you are writing what someone said, then it looks like this:

Kate said, "Put this in the oven." It goes inside the quotation marks.

If you are putting quotes around something to emphasize something:

John thinks he is being "cool". It goes on the outside because you are just using the quotes around that particular Word.

If you are quoting what someone said, the punctuation mark goes inside the quotation marks.