To agree with a positive statement:

We use so + auxiliary/modal verb + pronoun:

"I like tea without sugar.'
'So do I.'

To agree with a negative statement:

We use nor/neither + auxiliary/modal verb + pronoun:

"I don't like tea with sugar.'
'Nor do I.' or 'Neither do I.'

To disagree with a positive statement:

We use pronoun + auxiliary/modal verb + not (-n't):

"I like tea without sugar.'
'I don't.'

To disagree with a negative statement:

We use pronoun + auxiliary/modal verb:

"I don't like tea with sugar.'
'I do.'