Incorrect: We live in village.
Correct: We live in a village. OR We live in the village.

Incorrect: She works in pub.
Correct: She works in a pub. OR She works in the pub.

A singular common noun (e.g. boy, girl, tree, country, teacher, village etc.) must have an article. A plural common noun can be used with or without an article.

Incorrect: He is best player in the team.
Correct: He is the best player in the team.

Incorrect: She is fastest runner.
Correct: She is the fastest runner.

The definite article the must be used with superlative adjectives.

Incorrect: The Paris is big city.
Correct: Paris is a big city.

Incorrect: I live in the Mumbai.
Correct: I live in Mumbai.

If the noun is proper it will take no article. Note that a proper noun is the name of a particular person, place or thing. Examples are: Sam, Mary, India, Paris, London etc.

Incorrect: The iron is a useful metal.
Correct: Iron is a useful metal.

Incorrect: The gold is yellow.
Correct: Gold is yellow.

Articles are not used with material nouns. Examples are: gold, silver, iron, wheat, rice etc.

Incorrect: We should not make noise.
Correct: We should not make a noise.

Incorrect: I have an urgent business.
Correct: I have urgent business. OR I have some urgent business.

Note these fixed expressions.

Incorrect: Do you sell eggs by kilo or by dozen?
Correct: Do you sell eggs by the kilo or by the dozen?

The is used in measuring expressions beginning with by.