We can all speak and understand each other; do we need to investigate how?

Main clauses

The main clause is the group of words within a sentence that makes sense on its own. It tells us the main piece of information in that sentence. Any simple sentence will have only one clause. 

Steven opened the door.

It is usually quite easy, however, to pull out the main clause even from a complex sentence. Just ask yourself what the main piece of information is in the sentence.
Having finished his dinner, John put the dishes in the sink.
Claire, who was feeling unwell, went home for the evening.

Subordinate clauses

A subordinate clause is a group of words in a sentence, with a verb in it, which usually does not make sense on its own. It depends on the main clause for its sense. 
Having finished his dinner, George put the dishes in the sink.
Claire, who was feeling unwell, went home for the evening.
These clauses can be made as complicated as you want to make them. Just be wary of using too many of them as the meaning of the sentence can be lost.

5.4 Levels of syntactical analysis

Within the sentence we usually distinguish two syntactical levels of analysis, one belonging to the sentence proper, which is called the sentence level, and one belonging to various phrases treated as a whole and functioning in the sentence with the same force as separate words. This level is called the phrase level.

The subject and the predicate belong to the sentence level only. The object, the adverbial modifier, the attribute, and the apposition may belong either to the sentence level or to the phrase level.

He did not tell me anything about it. (Me, anything, about it are objects to the verb-predicate - the

sentence level.)
You are unhappy about something, aren’t you? (About something is an object to the predicative unhappy,
which is part of the predicate - the sentence level.)
He will come tomorrow. (Tomorrow is an adverbial modifier to the verb-predicate - the sentence level.)
You seem very tired. (Very is an adverbial modifier to the adjective tired, which is part of the predicate –
the sentence level.)
Poor Amy could not answer. (Poor is an attribute to the noun, which is the subject - the sentence level.)

In other cases objects, adverbial modifiers, attributes and appositions are included in various phrases within which they are not usually treated separately, the whole phrase functioning as part of the sentence on the sentence level.

He insisted on going by train. (On going by train is an object to the verb-predicate - the sentence level;

within the phrase on going by train we distinguish an adverbial modifier by train referring to the word-
form going - the phrase level.)

When analysing a sentence we deal mainly with the sentence level only, unless it is necessary for some reason to state the syntactical relations between the words within a phrase.