How are you supposed to use the ellipsis when writing a novel? Should there be spaces between every period, a space after the last word of the sentence?

An ellipsis is its own punctuation, a single mark, not three dots in a row.

Some word processors, like Word (at least on Mac), will automatically replace three periods in a row with an ellipsis if you type three periods. On the Mac, you can type an ellipsis by hitting Option-;. (There’s a way to do it on Windows too, but I don’t know what it is.)

If an ellipsis ends a sentence, yes, you put a space after it. If it’s inside a sentence, such as when you’re writing dialog where a person hesitates, then there’s no space after it.

You never type three periods with spaces in between; that’s not a thing.