Are there specific rules to build expressions with or without articles?

Some article use is idiomatic and has to be learned case-by-case. For example, we say:

• I'm learning to play the piano. (definite article)
• I had an egg for breakfast. (zero article)

In German conversely it's:

• Ich lerne Klavier spielen. (zero article)
• Ich aß ein Ei zum Frühstück. (zum = zu dem: dem = definite article)

There are nonetheless some useful guidelines that apply in most cases where a noun is used and hence a decision is to be made. Basically, this presupposes that you are able to determine if the noun is a count or uncount noun and whether or not you are referring to a specific (or known) instance of that noun. You will then be able to correctly choose the correct article in noun phrases such as in the following sentences such:

• There was an explosion at the station yesterday.
• There was an explosion at a station in the city center yesterday.

or

• Does he still go to school?
• Did his father go to the school yesterday.
• Is there a school near here?

A more detailed discussion would take up too much space, but if you are in doubt you are recommended to type the 3 basic possibilties for your phrase (play piano, play the piano, play a piano) into a search engine and analyse the results to see which choice best matches your own intended meaning.

You really need to consult a grammar book on this, particularly if you are not a native speaker of English, because the rules describing the use of articles are complex. Just to give you an idea, the 'Longman Student Grammar of Spoken and Written English' lists the following cases where the ‘zero’ article, that is, no article at all, is found:

Meals as institutions

Place as institutions

Predicatives with unique reference (a unique role or job)

Means of transport and communication Times of the day, months and seasons

Parallel structures (X and Y, or from X to Y)

Block language (as in newspaper headlines)

Vocatives