2. Either / or is used in a sentence in the affirmative (positive) sense when referring to a choice between two possibilities; meaning ‘this or that’ ; ‘he or she’ ; ‘one or the other’.
Examples:
Either John will go to Paris or Mary will come here.
He wanted to buy either a chocolate ice-cream or a butterscotch.
We can either eat now or after the show.
You can either go for a swim or play badminton. 
We should bring either coffee or tea.
Either you leave me alone or I will call the police.

3. Other uses of Either / Or
Either can also be followed by (one) of + group of two i.e.  you can use either of with a plural noun / pronouns
Either of us could do it (Either one of us could do it)
I don't know either of them very well.
There was no sound from either of the rooms.
Not… either… or denies both possibilities:
I don’t think either Mike or Lisa will be there.
He doesn’t speak either English or French.
Not… either is used after a negative statement.
I don’t speak French. You don’t either.
He isn’t ready to go. We aren’t either.

4. Neither / nor is used in a sentence in the negative sense when you want to say that two or more things are not true ; meaning ‘ not this nor that’ ; ‘not he nor she’ ; ‘not this one nor the other’.
Examples:
Neither Sarah nor Peter was to blame for the mistake.
I like neither apples nor oranges.
Jean liked neither Rome nor Paris. 
Neither Emma nor Susan gets on with Victoria.
There were neither cakes nor ice-cream at the party.
You can neither go by bus nor by taxi.

5. Other uses of Neither / Nor
Neither can also be followed by (one) of + plural noun i.e. i.e.  you can use neither of with a plural noun / pronouns
Neither of them is ready. (Neither one of them is ready.)
Neither of us has any money. Neither one of us has any money.
Neither is used like not… either.
When a negative statement has been made, you can use neither to show that this   statement also applies to another person or thing. You put neither at the beginning 
of the clause, followed by an auxiliary verb, a modal, or be, then the subject. You  can also use nor in the same way with the same meaning.
“I don’t speak French.” - “Neither do I.”
“He isn’t ready to go.” – “ Neither are we.”
David can't do it, and nor can Gavin.

6. Points to be Noted
The pairing Neither/Nor plays a negative role, so take care to avoid an unintended double negative, i.e. make sure your sentence does not have any other negatives preceding it. If you prefer to use a negative, then you should use either.
For example: He didn't find neither the map nor the key.  (WRONG)
He found neither the map nor the key. (CORRECT)
Neither is paired with nor and either is paired with or. You cannot mix them.  In other words, either cannot pair with nor, and neither cannot pair with or. But it is common to omit either from the either/or pairing.)

7. Singular or Plural
1. If both elements are singular, then the verb is singular too.
Either the father or the mother has to attend the meeting. (father and mother are singular; so the verb has is singular too)
Neither Leila nor Nancy is going to write the report. (Leila and Nancy are singular; so the verb is is singular too)
2. However, if one of the elements is plural, then the verb which is closer to the subject determines whether the verb will be singular or plural.
Either Sue or the girls are going to prepare dinner tonight. (the girls is plural; so the verb are is plural too)
Either  the girls or Sue is going to prepare dinner tonight. (Sue is singular; so the verb is is plural too)
Neither the teacher nor the students were in the classroom this morning. (the students is plural; so the verb were is plural too)
Neither the students nor the teacher was in the classroom this morning. (the teacher is singular; so the verb was is singular too)

8. Exercise : Choose the Correct Pair (Either / Or & Neither / Nor)
In this game, you __ win __ lose. It depends on.
___ Sue ___ Sara will help you with your homework.
This is my offer. You ___ take it ___ leave it.
When I go to the restaurant, I eat ___ fish ___ roast chicken. These are my favorite meals.
His father believed ___ his son ___ his friend. He thought that both were lying. 
I need ___ your help ___ your compassion. I can perfectly handle my problems all alone.
___ Charlie ___ Bill will write the report. Just ask one of them.
You can use ___ this computer ___ the other one. Someone must fix them first. 
Either /or
Either/or
Neither/nor