Either means one or the other of two. Neither means not either. Both either and neither are used to talk about two people or things. To talk about more than two people or things, we use none.
Study the following examples.
She has two kids. I haven’t seen either of them.
Neither of the keys would open the door.
She is a post graduate in history and political science. She can teach either of these subjects.
Neither of the watchmen was at his post. That’s how thieves broke into the premise.
There are two rooms on the upper floor. But there is no air-conditioning in either room.
Both of them knew the truth, but neither of them told me anything.
You can go by the front or the back door. Neither of them is closed now.
We have some bread and some cornflakes. You can take either.
Neither of my brothers is married.
We use a plural noun after either of and neither of. But the verb has to be singular.
Neither of them is here. (NOT Neither of them are here.)
This structure is used to make a negative addition to a negative statement.
Susan isn’t coming. Mary isn’t coming either.
He doesn’t like coffee. He doesn’t like tea either.
He doesn’t smoke. He doesn’t drink either.
Peter didn’t come. Mary didn’t either.
We can express the same ideas using neither
He doesn’t smoke. Neither does he drink.
Peter didn’t come. Neither did Mary.