New Text Formats

I’m interested in setting up different kinds of text formats.

For example, when I quote someone within an article, I’d like to have something that can either float to the left or the right (whichever looks better at the time) and in large font display a small excerpt of the post, but I do use the quote function the way it is right now, so I don’t want to change its formatting.

How would I go about creating a new kind of text formatting to get that working? For example, being able to easily click like “Interview Quote” and it’ll be formatted as that new quote type?