Previously mentioned
This is the simplest rule for the use of the article the. Look at the passage below:

There are a lot of trees in Mr Sato's garden. The trees are very old and many are twisted. Some of the trees form an arch over the gate.

In the second and third sentences the plural noun trees takes the article the, because of previous mention in the opening sentence.

Now look at the passage below:

Mr Kobayashi has pigs, cows, ducks and geese on his farm. The pigs live in a sty away from the house, while the cows graze in a pasture. The ducks and geese swim in a small pond behind the house. The animals are all happy and contented.

Note that when a plural noun is not previously mentioned (as in the first sentence) no article is used.
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The bookshelves in my office were knocked down by the earthquake.

We use the before the plural noun (bookshelves) because it is SPECIFIC -- my bookshelves. It also indicates that all of the bookshelves were knocked down.
If we want to indicate that some members of a group, but not all, did something, we use the construction 'of + the'. Look at the examples below:

Three of the boys went home (but the others stayed)

The three boys went home. (all of them)

Some of the children began to cry. (but not all of them)

Most of the researchers in Seishin could not go to work after the earthquake. (but some of them could)

A few of the computers were damaged in the earthquake. (but most of them were OK)

Some of the windows in Building #2 were damaged by the earthquake. (not all of them)
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EITHER OF
If you want to choose between two equal people, places or things, use the phrase either of + the,
e.g.

Either of the rooms will do. (it doesn't matter which room)

Either of the roads may be used. (it doesn't matter which road)

Note that you can say the same thing using a singular noun and no article,

Either room will do.
Either road may be used.

NEITHER OF
If you have two choices and don't like either of them, you can use the phrase neither of + the.

e.g.

Neither of the rooms will do. (they are both unsuitable)

Neither of the roads may be used.

As with either, you can use a singular noun and no article to say the same thing,

Neither room will do.
Neither road may be used

EACH OF
If you want to emphasize the individual members of a group, use the phrase each of + the.
e.g.

Each of the hens laid an egg.

Each of the students was given an assignment for the vacation.

As before, you can use a singular noun and no article to say the same thing.

Each hen laid an egg.

Each student was given an assignment.

NONE OF
The phrase none of + the is used to emphasize that no person, place or thing is excluded. Unlike other of + the phrases, this is the only way to express such a situation. We cannot re-phrase it using a singular noun.
e.g.

None of the employees got a raise last year.

None of the students did his homework properly.

None of the books were returned to the library.

ALL... / ALL OF
If you want to include every person, place or thing in your sentence, use the expression all. The article the is often used after all.
e.g.

All the houses in the street were damaged by the earthquake.

For extra emphasis use all of.
In this case you must use the.
e.g.

All of the houses in the street were damaged by the earthquake.

These expressions emphasise that there are no exceptions.

However, all can be used with plural nouns with no article. This style is often used with written commands:
e.g.

All students must pass the examination to graduate.
All foreigners must carry an I.D. card at all times.

You can also omit the article when you want to refer to a totality rather than units of a group:
e.g.
All rats (in the world) carry yellow fever.

but

All the rats in the lab died of a mysterious disease.

BOTH / BOTH OF
When you refer to two equal people, places or things, use the term both. You can use both without an article:
e.g.
Both boxes are too heavy to lift.
Or with an article for more emphasis:
e.g.
Both the boxes are too heavy to lift.
Or with of + the for even more emphasis:
e.g.
Both of the boxes are too heavy to lift.

MOST OF
Most of + the and a plural noun is used to mean nearly all, but not all items in a specific grouping:
e.g.

Most of the houses in this area were damaged by the earthquake.

Most of the researchers in Seishin had to take time off after the earthquake.

However we can omit the article and of  to refer to items in a group in a general manner:
e.g.
Most women like shopping for clothes.

SOME OF...
This expression is used to indicate more than a few but less than most. It is used with the to refer to people, places or things in a specific grouping:
e.g.

Some of the lab computer disks were damaged in the earthquake.

Some of the tables in the library were knocked over.

As with most you can use some without an article to refer to items in a group in general.
e.g.
Some men like doing housework.

ANY OF
This expression has a special usage. It is only used in questions and negative statements. With a common plural noun use the. With a plural pronoun, no article is needed:
e.g.

John: 'How about this topic? Could you understand any of the explanations?'

Bill: 'Sorry, no, I couldn't understand any of them.'

John: 'You couldn't understand any explanations? Oh my God!'

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