All, both, either and neither

“Both buses stop here” means the two do. “Neither bus stops here” means zero of the two do.

First count the options

Word	Number	Meaning
all	Usually three or more, or an entire group	Every member
both	Two	The two together
either	Two	One or the other
neither	Two	Not one and not the other

All three doors are locked.
Both doors are locked.
Either door is fine. (choose one)
Neither door is open.

For more than two choices, any or none is often more natural than either or neither.

Build the noun phrase

Before a noun, use both my friends, either answer or neither option. Before a pronoun, use of: both of them, either of us, none of them.

Both and all normally take a plural verb with plural nouns: Both students are ready. Either and neither usually take a singular verb with a singular noun: Neither student is ready.

Connect the word to the size of the group

Imagine two cafés, A and B. Both cafés are open means A is open and B is open. Neither café is open means A is closed and B is closed.

Either café is fine means you can choose A or B. It does not mean only one is suitable; it means each is an acceptable choice.

For three cafés, use All three cafés are open, Any of the three cafés is fine, or None of the three cafés is open. Both/either/neither are normally used for a pair in these choice patterns.

A noun and a pronoun use different patterns

With a noun	With an identified group	With a pronoun
both cafés	both of the cafés	both of them
either café	either of the cafés	either of them
neither café	neither of the cafés	neither of them
all cafés	all of the cafés	all of them

Both the cafés and all the cafés are also natural; of is optional in these patterns. With a personal pronoun, keep of: both of us, not ~~both us~~.

After either/neither directly before a countable noun, use singular: either route, neither answer. Both takes a plural noun: both routes.

The meaning changes quickly

Either train goes to the airport. Each of the two trains is a possible choice.
Neither train goes to the airport. You need another route.
Both trains go to the airport. You can take either one.

This small set of words is useful for giving clear choices and avoiding misunderstanding.

Agreement follows the construction

Both students are ready has a plural subject. Neither student is ready has a singular noun.

With neither of the students, singular is is a useful choice in careful writing. Plural are also occurs in everyday English when speakers think of the people as individuals. Do not treat every plural verb after neither of as an impossible form.

All can refer to uncountable material too: All the water is cold. The noun water, rather than the word all alone, gives the singular agreement.

Keep “not all” separate from “none”

Not all the doors are open means at least one door is closed. It does not tell you exactly how many are open. None of the doors are open explicitly means zero are open.

For two doors, Neither door is open is clear. Avoid Both doors aren't open when you need to distinguish “neither” from “not both”; readers may understand the negative scope differently.

You can join alternatives with either ... or: We can meet either on Monday or on Tuesday. Use neither ... nor to exclude both: Neither Monday nor Tuesday works for me. The joined items should have parallel forms: two days, two noun phrases or two clauses.

Make a practical decision

A: Which of these two buses goes to the museum?
B: Both do. You can take either one.
A: Are they both direct?
B: No. Neither bus is direct; you'll need to change.

The replies distinguish destination from route. Both answers about the pair; either offers a choice; neither excludes a property from both.

Count the options first, then decide whether you mean every member, a choice from the pair, or zero of the pair. That gives each word a clear purpose.