So, neither + auxiliaries

Use So do I / Neither do I, etc. to say that you have something in common with somebody.
I love football. So do I.

Use So + auxiliary + I with positive sentences.
I'm happy. So am I.

Use Neither + auxiliary + I with negative sentences.
I'm not hungry. Neither am I.

The auxiliary you use depends on the tense.
I love basketball. So do I.
I didn't like the film. Neither did I.
I can run. So can I.
I wasn't very happy. Neither was I.
I've been to Germany. So have I.
I wouldn't like to go to the disco. Neither would I.