To agree with a positive sentence, say So + the same helping word (am, do, can, have) + I.
So ... I, to say me too
I'm hungry. → So am I!
I like pizza. → So do I!
She can swim. → So can I!
Not "I like pizza. So like I!" — say "I like pizza. So do I!". After So, use the helping word do, not the main word "like".
Try it: I like this song. Agree with this. (Leave out the words you don't need.) Answer: So do I. — It is positive, so start with So, and use the helping word do (not the main word "like"): So do I. "Neither" is for negative sentences.
Neither ... I, to say me neither
To agree with a negative sentence, say Neither + the same helping word + I. There is no extra not, because Neither already means not.
I'm not tired. → Neither am I!
I don't like coffee. → Neither do I!
She can't drive. → Neither can I!
Not "I'm not ready. So am I." — say "I'm not ready. Neither am I.". The first sentence is a no, so agree with Neither, not So.
Try it: I can't swim. Agree with this. (Leave out the words you don't need.) Answer: Neither can I. — It is negative, so agree with Neither + can + I: Neither can I. No extra "not" or "can't" is needed, because Neither already means not.
Use the same helping word
Take the helping word straight from the sentence: am → am, can → can, have → have, was → was, were → were. When the sentence has no helping word, borrow one: do for now (I like → So do I), did for the past (I went → So did I).
I am ready. → So am I.
I have been to Senfarren. → So have I.
I can cook. → So can I.
I was tired. → So was I. · We were late. → So were we.
No helping word? I like pizza. → So do I. · I went home. → So did I.
Try it: I went to the market on Saturday. Agree with this. (Leave out the words you don't need.) Answer: So did I. — "Went" has no helping word and it is the past, so the helping word is did: So did I. You do not repeat the main word (not "So went I"), and have is for the have/has form (So have I).
Try it: I have been to Senfarren. Agree with this. (Leave out the words you don't need.) Answer: So have I. — The sentence uses have, so your answer uses have too: So have I. The helping word matches, so it is not "do" here.
Try it: I'm not hungry. Agree with this. (Leave out the words you don't need.) Answer: Neither am I. — It is a no (not hungry), so agree with Neither. And the sentence uses am, so match it: Neither am I. "So" is for positives, and "do" does not match am.