As a pronouneither is used to mean a choice of one or the other of two people or things.
As a pronounneither is used to mean not one and not the other.
 

Either and neither are used before of followed by a plural noun. 

Examples:

  • I am going to have a tattoo on either of my arms.
  • You can have either of these buns; one is for your brother.
  • Neither of her parents approves of her staying out late night after night.
  • Those are twin sisters. Neither of them wants to separate from the other.

 

Either and neither must not be used in front of a plural noun or pronoun without of

Examples:

  • She's angry with both of us or either of us.
    Not: She's angry with both of us or either us.
  • The scream came from neither of the houses across the road. (Two houses)
    Not: The scream came from neither houses across the road.

 

Either and Either of have same meaning
There is no difference in meaning between either preceding a noun (determiner) and either of (pronoun) preceding a plural noun.
  • I’m giving away either kitten. = I’m giving away either of the kittens.
 
Either and Neither are singular
Either and neither are singular subjects, so the verb that follows them has to be singular.
 

Examples:

  • Police are questioning the two suspects as either of them is the real killer.
  • Either of the twin brothers has a big mole on the chest. 
  • Neither of the two small donkeys is ready to carry heavy loads.
  • Neither of the buses plying this route carries many passengers at this time of night. (Two buses)

 

Either and Neither on their own
Because either and neither are used as pronouns, each of them can be on its own.

 

Examples:

  • These two? I don't want either.
  • Do you want to ride this camel or that one? Either, I like riding camel.
  • Which of your shoes is missing? Neither, I have found the missing one.
  • "Do you want a coffee or a tea?" "Neither. Thanks."

 

Either and Neither in negative statements
Either of can be used in negative statements to emphasize both of two people or things. When using neither in a negative sentence, a negative verb must not be used, as both negatives together will give a positive idea. In place of it, we use either.

 

Examples:

  • She doesn't like either of them. = She doesn't like them.
  • No: He doesn't want to take neither of these pills.
  • Yes: He doesn't want to take either of these pills. 

 

Neither and ‘both … not …’
We need not use “both … not … “ all the time. We can use neither instead.

 

Examples:

  • Both of them do not know how a ghost looks like.
  • Neither of them knows how a ghost looks like.