You would use neither with: 'nor' (neither she nor he ate biscuits) - negative
You would use either with: 'or' (either she ate a biscuit or he did) - positive
In the above:
Neither is none of them did
Either is one or the other did
Answering a question like, "which out of these two dresses should I buy?"
Neither. (None of those)
Either. (One or the other)
Using either in a statement:
I agree, I don't like that dress either. (Yes)
Either one will look great on you. (either as in one or the other)
I don't like either of those dresses (both)
Using neither in a statement:
Neither do I, that dress is terrible. (No)
Neither look good on you. (Both-negative)
I like neither of those dresses (none)