I know that in Russian there are no articles, so I'll simplify things but this should give you some general ideas about where they're necessary.
The articles can be of two types: Determinate (THE) or Indeterminate (A/AN). The main difference is that THE refers to ONE specific object, and A/AN refers to ANY object. For example, if you tell your friend to sit in A chair, this means he can sit in any chair he wants. If you tell him to sit in THE chair, then there are two options: 1) there is only one chair to choose from, or 2) he knows which chair he should sit on.
The nouns can also be of two types: Countable (can be counted, 1, 2, 3, many: car, book, chair, etc), and Uncountable (can't be counted, you could have "some", but not any number: for example: air, water, information)
- Can not have an indefinite article: You can't have "a water", or "an information".
- Can have an definite article, this means a specific instance. For example: the water in this river is dirty (not ALL the water, but only the water in this river!). The information which this man has is false (not all the information in the world, but only the information which this man has).
- Can have NO article, when it is mentioned in general, not a specific instance. For example: Water is good for you. Information is power.
- In SINGULAR: they MUST have an article. Determinate THE when you refer to one object in particular: Give me the book (either there is only one book, or we both know which book you are talking about). Indeterminate A/AN when you're not referring to one object in particular: Give me A book = give me one book, I don't care which book you choose.
- In PLURAL: they can't have A/AN. But they can have THE or they can have no article. THE is used when you refer to a specific group: The chairs in this room are comfortable. The cars in this shop are expensive. NO article is used to refer to ALL in general: Guns can kill.