I use 'so do I' to say that a positive sentence is also true for me, and I use 'neither do I' to say that a negative sentence is also true for me:
John: I hate mushrooms.
Me: So do I (=I also hate mushrooms).
Lucy: I don't live in London.
Me: Neither do I (=I also don't live in London. For example, maybe Lucy and I both live in Paris).
Present simple: use 'do / does'Lucy likes coffee. So do I.
Lucy doesn't like coffee. Neither do I.
Present simple with 'be': use 'am / is / are'John's at the office. So am I.
John isn't at the office. Neither am I.
Present continuous: use 'am / is / are'Luke's going out tonight. So am I.
Luke isn't going out tonight. Neither am I.
Past Simple: use 'did'Jill went to the cinema yesterday. So did I.
Jill didn't go to the cinema yesterday. Neither did I.
Past simple with 'be': use 'was / were'She was at the library. So was I.
She wasn't at the library. Neither was I.
ALL TENSES:
Slide 3
Present perfect: use 'have / has'They've been to Colombia. So have I.
They haven't been to Colombia. Neither have I.
Future simple: use 'will'Edward will be at the cafe later. So will I.
Edward won't be at the cafe later. Neither will I.
Modal verbs: repeat the modal verbHe would like a cup of tea. So would I.
He wouldn't like a cup of tea. Neither would I.
Emma can speak Russian. So can I.
Emma can't speak Russian. Neither can I.
Slide 4
We can also use 'I do too' and 'I don't either', which mean the same as 'so do I' and 'neither do I':
John: I hate mushrooms.
Me: I do too (=I also hate mushrooms).
Lucy: I don't live in London.
Me: I don't either (=I also don't live in London).
We can also use 'me too' and 'me neither'. 'Me too' has the same meaning as 'so + auxiliary verb + I' and 'me neither' has the same meaning as 'neither + auxiliary verb + I'. 'Me too' and 'me neither' are very informal:
John: I hate mushrooms.
Me: Me too (=I also hate mushrooms).
Lucy: I don't live in London.
Me: Me neither (=I also don't live in London).
We live in London and so do they.
Emma loves tennis. Jill and Laura do too.
My parents don't come here often. Neither does Alex.
She isn't French and neither is he.
You don't like cold weather. Neither do we.