Improving your writing:
Countable and uncountable nouns

Most nouns in English are 'countable'. Countable nouns are objects that can be counted. Examples would be 'dog', 'car', 'apple', 'document'. Each dog or apple exists by itself. It is separate, and different from, all other dogs or apples.

When countable nouns are in the singular, they cannot stand alone. They MUST follow 'a/an', 'the', 'my', 'this' etc. This is a point which is difficult for native speakers of Japanese. When you write English be careful to check that you have not left any singular countable nouns without 'a/an', 'the' etc.
For example: I am a student at a university in Yokohama.

Remember that you need 'a' etc. even if there is an adjective in front of the noun:
I am a student at a well-known university in Yokohama.
I am a student at the biggest university in Yokohama.

However, some nouns in English are 'uncountable'. They cannot be counted, and have no plural. They are more similar to nouns in Japanese. Note that in dictionaries, uncountable nouns are identified by [U].
They tend to belong to one of the two following categories.

a) substances considered generally, such as 'bread', 'milk', 'plastic', 'snow' etc. Milk exists as a mass; it is not made up of separate pieces. It is not possible to distinguish between one bit of milk and another bit of milk.

These nouns can stand alone. They NEVER follow 'a/an', but they can follow 'the', 'my', 'this' etc.
I have bread for breakfast.
I drink milk before I go to bed.
Where is the milk I bought yesterday?
This plastic can be recycled very easily.
If you wish to count this type of uncountable noun, you need to separate them into countable portions first. This is done by using counters, as in Japanese.
For example, bread is counted in loaves, slices etc.
I bought a loaf of bread today.
We will need three loaves of bread to make all those sandwiches.
He ate five slices of bread spread with butter and jam.
I swept away the crumbs of bread that had fallen on the floor.
Liquids such as milk, water, and rain are counted in cups, litres, jugs, drops etc.
When I was pregnant I drank three cups of milk every day.
There are a few drops of milk left in the jug.
Adults should drink two litres of water a day.
The first drops of rain made a pattern on the dusty road.
b) abstract nouns such as 'economics', 'health', 'golf', 'information'. These are concepts, and do not exist as objects that can be touched. They NEVER follow 'a/an', but can follow 'the', and possibly 'my', 'this' etc. Some of them can be counted.
I am studying economics at Keio University.
The economics that I am studying at Keio is very interesting.
My golf has improved since I began practising every day.
This information will be extremely useful.
This is a very useful piece of information.

For a colorful list of different types of uncountable noun, see Types of Non-Count Nouns by Brenda Sansom-Moorey of Georgia State University.

Some nouns can be either countable or uncountable, depending on their meaning. In dictionaries, [U] is used to show their meaning as uncountable nouns, and [C] is used to show their meaning as countable nouns. Normally they are uncountable when used in a general, abstract meaning (when they do not exist as separate objects) and countable when used in a particular meaning (when they exist as objects that can exist separately).
Obvious examples are 'fruit' , 'sport' and 'wood'.

Fruit/Sport is good for you.
The kiwi is a fruit that originated in New Zealand.
I learnt three sports at school: tennis, hockey, and netball.
This looks like natural wood, but it is plastic.
This looks like a natural wood, but it is a plantation.

There are less obvious examples, such as 'success' and 'chicken'.

'Success' is normally uncountable, and refers to 'the state of having achieved a goal/fame/high status etc.'.

For an athlete, success is a gold medal at the Olympics.
For several months after her success at the London Olympics, where she won five gold medals, Helen made regular appearances on television.

As a countable noun, 'success' refers to 'a person or thing that has been successful'.

She was a success as an athlete, but not as a television personality.
His first film was one of the surprise successes at this year's Yokohama Film Festival.

'Chicken', on the other hand, is normally countable, and refers to the whole animal (either alive or dead).

I saw a chicken crossing the road.
I saw some chickens running away from a fox.
I'll order a chicken for Christmas lunch if you help me to cook it.

When chicken is cut up for food, however, it loses its separate, individual identity and therefore becomes uncountable.

I'll buy some chicken for lunch.
I'd like 200 grams of chicken please.

Note the following differences/similarities between the way in which countable and uncountable nouns are used. Note also that 'counter + uncountable noun' is used in the same way as a countable noun.

'Some' and 'a lot of' can precede both, but the uncountable noun does not become plural.
I ate some grapes.
I drank some water.
I bought some bottles of water.
A lot of documents were found.
A lot of information was found.
'Many', 'few', and 'a few' precede countable nouns; 'much', 'little' and 'a little' precede uncountable nouns.
They have already read many/ a few books/ boxes of information.
They have already discovered much/ a little information.
As a result of the drought, there are few rivers left in this area.
As a result of the drought, there is little water left in this area.

Click for explanations and quizzes about the use of "a", "the" and countables, uncountables and problems with them from the British Council learn English website. (See also the teenagers' version.) This may also be helpful.
Here and here are two quizzes on countables and uncountables, from Pearson Brown's better english.com.
Are these nouns countable, uncountable, or both? (by Jill Cosh, Anglia Ruskin University), and a similar one from the Capital Community College Guide to Grammar and Writing.