Both, Neither, Either

Use:

1) Both
Both means two of two things.
I have two cats. I like both of them.

2) Neither
Neither means not one or the other of two things.
Neither of my cats is grey.
Remember to use a singular verb after neither.
Neither of the dogs are dangerous. => Neither of the dogs is dangerous.

3) Either
Either means one or the other.
There are two cakes. Please have one. You can have either one.

Form:

1) You can use both, neither and either directly before a noun.
Both supermarkets are good.
Neither supermarket sells electrical goods.
We can go to either supermarket, I don’t mind.

2) Both, neither and either are often used with ‘of’. But you must always use a determiner(the, my, these, those, his etc) before the noun.

Both of children like chocolate cake. => Both of the children like chocolate cake.

However, you don’t have to use of with both.
Both of the children like chocolate cake. 
Both children like chocolate cake.

3) You can use both, neither and either+ of + object pronoun(you, them, us).

Both of them wore white dresses.  
Neither of us was late.  
Have either of you got a pen?

4) You can use both ... and ...; neither ... nor ..., and either ... or ....
Examples:
Both James and Diana work here.
Neither James nor Diana works here.
You can ask either James or Diana.

Practice 1

Practice 2

Practice 3