"Either" and "neither" are both singular adjectives meaning "one or the other of two." "Neither" of course means "not the first one and not the second one."
In formal writing, we usually use a singular verb because "either" and "neither" signal that one of the following nouns is the subject, but not both:
Either Bill or Bob is going to the conference. (One or the other is going, but not both.)
Neither Joan nor Jane likes sushi. (= Joan doesn't like sushi. Jane doesn't like sushi either!)
Notice that we say "either...or" and "neither...nor." In informal English, most people would say "Neither Joan OR Jane LIKE sushi." That's all right in conversation, but in formal documents you should prefer the formal usage.
Of course we have a confusing exception to this rule. You can use a plural verb if you have a plural noun next to the verb:
Either Joan or the Kennedys are going to the conference.
But put the singular noun closer to the verb, and it goes back to singular!
Either the Kennedys or Joan is going to the conference.
And it's the same with "neither":
Neither Jane nor her brothers like sushi.
Neither her brothers nor Jane likes sushi.
Of course the verb will be plural if both nouns are plural:
Either the Smiths or the Robinsons are meeting us at the station.
Neither the Canadians nor the Americans are interested in this problem.
Más Ejemplos:
I like neither of them.
No me gusta ninguno.
Neither of you will go and that's it!
¡Ninguno de ustedes irá y eso es todo!
a.- Peter can't read
b.- Neither can Bob.
a.- Peter no puede leer.
b.- Bob tampoco.
También tiende a usarse en conjunción con 'nor', lo que vendría siendo "ni____ni..."
Neither this or that one, both are awful.
Ni éste ni aquel, ambos son horribles.
They will neither stay nor help the rest of the class.
Ellos ni se quedarán ni ayudarán al resto de la clase.
Ten en cuenta que "neither” es una palabra negativa de por sí y no puede usarse en oraciones que ya son negativas; recuerda que “neither” convierte las oraciones positivas en negativas.