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A.  How to determine whether a noun is countable or uncountable when it can be used as either? 

(1) The difference lies in how and where you use the word, whether it means something in general or different types of a certain thing.

For example:

There are several (types of) doctrines in the world, such as the various religious doctrines and military doctrines.

There are several (types of) religions in the world, such as Buddhism, Christianity, Islam, etc.

There are so many different (species of) fishes in the world.

Doctrine (in general) provides discipline and directions for human beings to follow.

Religion (in general) teaches human beings to stay away from violence.

Fish (in general) has tons of omega-3 fat that is good for your health.

(2) You can also think of it as abstract vs. concrete.

For example: 

Countable -

(a) The doctrine of the Catholic Church.
(b) The Monroe Doctrine and the Declaration of Independence are two famous doctrines of America .

Using the word “doctrine” as a countable noun, we mean a particular principle, instruction, position, or policy taught or advocated by its adherents scientific or social doctrines, as of a religion or government.

You can argue that the doctrine of the Catholic Church is a particular principle taught by the Catholic Church. And there could be different doctrines taught by the Catholic Church. When we said "the" doctrine of the Catholic Church, we are referring to this specific doctrine.

Uncountable -

(c)  Example moves the world more than doctrine.

Use the word “doctrine” as an uncountable noun, when used in a general, abstract meaning. Here we are talking about something that is abstract, some concept.

Other example:

(i) Life is full of ups and downs.
(ii) Several lives were taken at the 911 tragedy.

Life is used as an uncountable noun when referring to life as an abstract concept, but is used as a countable noun when referring to individual lives.

B.  How to determine if a noun is countable or uncountable?
A rule of thumb is to think of whether the thing can be counted or not.  If it is abstract, it is uncountable. 

Some mass nouns (集合名詞) are uncountable such as (1) inseparable, indistinguishable particles or unholdable materials without a container, or (2) generic items grouping together for their similar functions as in “furniture” and “silverware”.

A countable noun takes either the indefinite (a, an) or definite (the) article when it is singular. When plural, it takes the definite article if it refers to a definite, specific group and no article if it is used in a general sense. 

Uncountable nouns cannot be counted.  They have only a singular form and do not take the indefinite article (a, an) before them.  If referring to something specific, you can use the definite (the) article.

For example:

Countable –

I saw many kids playing in the park last week.

There is only a kid playing in the park now.

I like eating grapes.

Grapes contain lots of vitamins.

Uncountable -

Wine is not good for you.

The wine I am drinking contains over 40% alcohol.

I like eating rice.

Rice is good for our health.

C.  Can uncountable nouns be counted?

Yes, if you add unit nouns in front of them

For example:

1. a piece of meat/cake

2. a cube of sugar

3. a bolt of lightning

4. a bar of soap

5. a grain of ice
6. a slice of bacon

7. a loaf of bread

8. a cup of juice/tea

9. a jar of jam

10. a tube of toothpaste

11. a pitch of water

12. a box of cigarettes

13. a bag of flour

14. a bottle of mineral water

15. a carton of milk

16. an alloy of gold

17. a yard of cloth

18. a dose of medicine

19. a barrel of oil

20. a pint of milk

21. a piece of information/research/knowledge/news

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Here are some websites where you can find more information around this topic.

http://web.hc.keio.ac.jp/~hjb/countable.uncountable.html  

http://www.wordpower.ws/grammar/gramch16.html   

http://owl.english.purdue.edu/handouts/print/esl/eslcount2.html