These are used to compare or contrast things.
Neither is used to say you are, or it is, not something.
The water is neither cold nor hot. It is comfortable.
He was neither early nor late, but on time for the meeting.
Either is used to say you are, or it is, something.
The water is either cold or hot, but never comfortable.
He is either early or late, but never on time.
Hope that helps a little! :)