SO 

SO is used to show agreement with affirmative statements by, or concerning, another person.

SO + Auxiliary + Subject (pronoun) :  So do I

Remember :
The Auxiliary in the response must agree with the verb tense in the original statement.

Here are some examples :

Speaker ASpeaker B
Charlie likes chocolate.So do I= I like chocolate too.
Emma lives in London.So does Amanda.= Amanda lives in London too.
Alex can swim.So can Jenny.= Jenny can swim too.
Pedro is good at sports.So is Rafael.= Rafael is good at sports too.
Our teachers are very strict.So are ours.= Our teachers are very strict too.
Enzo would love to work in Paris.So would I.= I would love to work in Paris too.
Alex will be angry.So will I= I will be angry too.

NEITHER 

NEITHER is used to show agreement with negative statements.
NEITHER can be replaced by NOR with no change in meaning.

Neither + Auxiliary + Subject (pronoun) :  Neither do I (Nor do I)

Remember :
The Auxiliary in the response must agree with the verb tense in the original statement.

Here are some examples :

Speaker ASpeaker B
Sam doesn’t want to go out.Neither do I.= I don’t want to go out either.
Wendy can’t cook.Neither can I.= I can’t cook either.
Jason doesn’t have a ticket.Neither does Tom.= Tom doesn’t have a ticket either.
I can’t speak Chinese.Neither can Julie.= Julie can’t speak Chinese either.
Peter hasn’t finished yet.Neither has James.= James hasn’t finished yet either.
Meg couldn’t come today.Neither could Amy.= Amy couldn’t come either.
Dad won’t pay attention.Neither will Mum.= Mum won’t pay attention either.