A conjunction is basically a word which connects phrases, words, clauses or sentences. It also brings the relationship between elements which are thus joined. It also brings about relationship between the elements which are thus joined. There are two types of conjunctions:

Co-ordinate conjunctions
Subordinate conjunctions
A co-ordinate conjunction joins clauses or sentences of equal rank. Also, it joins words of equal grammatical rank.

[And, but, for, nor, or, but, otherwise, else, also, either -or, neither -nor, etc. are the chief co-ordinate conjunctions. For instance;
She went to the hospital and met the doctor.

Drake and Dragon are best friends.

The Co-ordinate Conjunctions are of four kinds:

1. Cumulative Conjunctions: A conjunction which adds one statement or fact to another is a cumulative conjunctions. For instance;

The professor as well as the lecturer has accepted to conduct the examination next week.

The following are the cumulative conjunctions:

Not only —but also,
Both — and,
As well as
too, also, moreover, etc.
2. Alternative Conjunctions: A conjunctions of this kind expresses a choice between two alternatives. Either–or, neither–nor, otherwise, else, etc. are alternative conjunctions. For instance;

He is good neither at games nor at studies.
Work hard, otherwise you will fail.
3. Adversative Conjunctions: An adversative conjunction expresses a contrast between two facts or statements. Only, however, but, still, yet, whereas, nevertheless, etc. are adversative conjunctions. For instance;

He was angry, but she kept quiet.
He hates me, yet I love her.
4. Illative Conjunctions: Such a conjunction shows that a statement or fact is proved or inferred from another. Therefore, hence, so, consequently, for, etc. are Illative conjunctions. For instance;

She is honest and amiable, hence he is revered.
5. Subordinate Conjunctions: These are the conjunctions that connect a clause to another on which it depends for its full meaning.

The adverbial clauses are usually connected to the main clauses by means of the subordinate conjunctions: The Chief Subordinating Conjunctions are after, because, if, another, through, till, etc. The following are some of the sentences in which important subordinate conjunctions are used.

She had died before the doctor arrived.
We eat so that we may live.
She behaved in such a manner that all dislike her.
The following compound expressions also can be used as conjunctions. For instance; In order that, on condition that, even if, so that, provided that, as though, as well as, as if, etc.

P.S. : There are some words which are used both as conjunctions and as prepositions.

Conjunctions – [We went home after she came to the office.]
Prepositions – [We went home after sunrise.]
Conjunctions – [I went to bed early, for I was tired.]
Prepositions – [I shall do it for him.]
The following conjunctions are used in pairs and hence are called correlative conjunctions.Rules for Conjunctions - English Study Material & Notes

Either—or
Neither—nor
Both—and
Though—yet
Whether—or
Not only—but also
When conjunctions are used as correlatives, each of the correlated words  should be placed immediately before the words ti be connected.

For instance;

She not only visited Delhi but also Jaipur. [Is WRONG]
She visited not only Delhi but also Jaipur. [Is CORRECT]
She is neither good at Mathematics nor at Science. [Is WRONG]
She is good at neither Mathematics nor Science. [Is CORRECT]

 Coordinating Conjunctions

A coordinating conjunction joins words, phrases or clauses having similar grammatical structure.

A coordinating conjunction is also called a coordinator, which are ‘but, and, or, so, nor, yet, for’.

It joins the following:

    Word + Word
    Phrase + Phrase
    Clause + Clause 

Read the following example, the underlined parts are the words, phrases and clauses joined by the coordinating conjunction such as ‘and, or, but’
Examples:

He bought a book and a pen.                                                      (two words)
I forgot to bring my laptop and camera.                              (two word)
You may meet me at my home or at my office.                (two phrases)
He always sits in the library or in the classroom.           (two phrases)
I waited for him but he didn’t come.                                       (two clauses)
She requested him for help but he didn’t help her.        (two clauses)

It can be seen in the above examples, the words, phrases and clauses joined by coordinating conjunctions, in each sentence, are of similar grammatical nature.

  Subordinating Conjunctions

A subordinating conjunction joins a subordinate (dependent) clause to a main (independent) clause.

A subordinating conjunction is also called subordinator, which are ‘although, because, before,  if, how, since, once,  till, until, where, when ,whenever,  whether, after, while,  no matter how, provided that, as soon as, even if’

    Main Clause + Subordinate Clause
    Subordinate Clause + Main Clause. 

A main clause is a group of words having a subject and a verb. A main clause can stand alone as a sentence because it can give complete meaning. On the other hand, the subordinate clause cannot stand alone as a sentence as it does not give complete meaning. It depends on main clause to give complete meaning.

The subordinate clause starts with subordinating conjunctions as shown by the underlined words in the following examples.

The parts of following sentences in red color are main clauses. The part of sentence in blue color are subordinate clauses.

Examples:

You will succeed in life provided that you think optimistically.
We went to zoo where we saw an elephant.
I will help whenever you need my help.
All the shops were closed because it was late.
It makes me happy when you laugh.
I will not tell him the secret even if he insists a lot.
Although It is raining, it is too hot today.
As far as I know, he is a very nice person.
If you avoid sugary foods, you will lose your weight.

  Correlative Conjunctions

Correlative conjunctions are paired words. It joins words, phrases or clauses having reciprocal or complementary relationship.

The common correlative conjunctions are as follows:

    Either …. or
    Neither .… nor
    Whether.… or 
    Both …. and
    Not only .… but also 

Examples:     

He may buy either a laptop or a camera.
She likes neither tea nor coffee.
Both the pink and the blue are nice colors. 
She is interested not only in singing but also in games.
You will find him either in the library or in the classroom.