Countable nouns can be counted. In English it is important if there is ‘one’ (singular) or ‘more than one’ (plural).
The singular noun is simply the base form of that noun, for example: pen, baby, bus, potato, piano.
If there is more than one then we need to use the plural. Most plurals are formed by adding ‘s’ or ‘es’ to the base noun, for example: pens, babies (don’t forget ‘y’ changes to ‘i’), buses, potatoes, pianos.
Some nouns (but not all) which end in ‘f’ change the ‘f’ to ‘v’ and add ‘es’, for example: wolf/wolves, knife/knives, shelf/shelves.
This should be pretty easy for most of you, but you need to be careful because there are a few irregular nouns, for example:
child/children, foot/feet, mouse/mice, tooth/teeth, person/people, woman/women.
Though I think you probably know most of these too. But don’t forget that some nouns have the same singular and plural forms, for example:
sheep/sheep, fish/fish, series/series, crossroads/crossroads.
And there are some plurals which are very strange, for example:
bacterium/bacteria, cactus/cacti, criterion/criteria, fungus/fungi, medium/media, oasis/oases, stadium/stadia, vertebra/vertebrae.
And finally there are some nouns which have no singular, and are plural only, for example:
clothes, congratulations, goods, manners, police, savings, thanks.
Plus many nouns which are considered to be in a ‘pair’, which are also plural only, for example:
scissors, pants, tights, jeans, binoculars, spectacles and scales.
However we say ‘no pens’ or ‘no babies’, so zero is plural! But six babies are better than no babies, so please look at the sextuplets below.
thiNK TWice 
Can you please talk on nouns which can be both countable and noncountable? Thanks.
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That’s a huge topic zikher.
My views are slightly unconventional here, since I believe that virtually every non-count noun can also be countable in certain contexts. The distinction between count and non-count is primarily conceptual, the grammatical difference being simply the fallout.
I will try to write something soon.
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Thanks to Kouta and Kim for their very helpful points.
Even though Kouta has never neede to use the word mitochondrion I think he might use it in the future if human cloning ever happens.
I could never see the reason for distinguishing singular from plural until I read Kim’s comment, thanks for helping me to think twice!
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The Little Prince lives on an incredibly small planet. He has a single rose on the planet. The flower is very beautiful, and he came to like her. But she annoyed him sometimes and he was confused. One day the prince decided to take a leave from the planet to spend some time alone.
When he visited the earth, he was surprised and bewildered to find lots and lots of roses. But after he made friends with a fox, a snake and a human, he realized that although the rose on his planet is one among many, she is still special to him for she is the one and only rose he made friends with.
There are millions of stars in the universe, but there is only one planet on which the Little Prince smiles. Because of that one tiny little planet, when we look up at the night sky, we feel a little happiness.
So special is “being one”, that we clearly distinguish Singular from Plural and never leave a singular noun without a crown: “a/an”, “the”, “my” etc.
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Fish or Fishes. – Both are correct plural forms of the singular word Fish.
Shego
Fishes live in the sea, as men do a-land; the great ones eat up the little ones.
William Shakespeare
And the Lord said to her, “Two nations are in your womb, and two peoples, born of you, shall be divided; the one shall be stronger than the other, the elder shall serve the younger.”
Genesis 25:23
When they say “peoples”, they don’t count individuals but groups like “two peoples in Japan, namely Japanese and Ainu”. The same goes for fishes.
“Persons” is used in formal expressions.
This vehicle is licensed to carry 4 persons. (= in a notice)
(law) The verdict was murder by a person or persons unknown.
Oxford Advanced Learner’s Dictionary
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I often forget to add “s” or “es” to the base noun.
I know an example of strangely-changed noun too.
It’s mitochondrion/mitochondria.
This pattern is the same as criterion/criteria.
By the way, I’ve not used this noun in my life.
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