• We use either to say about one OR the other of two persons or things.

EXAMPLE: I have viewed both houses but I don't like either one very much.

• We use either to mean the one AND the other of two people or things.

EXAMPLE: There is a door at either end of the room.

• We use either to show one or the other thing is happening.

EXAMPLE: Either he is telling the truth or you are.
EXAMPLE: Either you are going, or I am.

• We use either or neither for two things. We use these words with a noun.

EXAMPLE: We can ride either horse. (either horse = a noun, so we do not say 'either horses; either = this horse or the other horse. I don't mind riding one of them.)
EXAMPLE: Neither book is mine. ('Neither book' is treated as a noun, 'is' not 'are' is used. The sentence means both the books are not mine.)

• We use neither to mean not this one AND not the other one of two people or things.

EXAMPLE: Neither twin wants to be physically separated from the other.
EXAMPLE: He is not telling the truth, neither are you.