It doesn't make any sense to discuss about the basic meaning of preposition, however "intuitivly" they have one, otherwise we couldn't use them in unknown circunstances. One basic meaning of de is to describe the source, the stream of something from somewhere to somewhere. In this meaning from it is translated with de.
He learned it from his aunt.
He got the money from him.
Don't expect to get any answers from him.
Furthermore de describes to whom something belongs.
This is the car of my father.
This is the door of the house.
It is not very clear how one gets from source / origin to belonging, but the use of de to describe to whom something belongs to seems "intuitive", otherwise the genitive, my father's house => the house of my father, wouldn't have been substituted by of / de. If in any langguage the same preposition is used, in other words the corresponding one, then we can't say that it is arbitrary. (To be more precise: If in different languages the genitive is formed with prepositions who are very often used in the same context even if the semantic motivation is weak, it can't be arbitrary.) .
de + article becomes da, do, dos, das, see 4.2.1. As a rule of thumb we can say that ther is no article if there is none in English.
Quando um grupo de turistas visita uma cidade tem ares de quem visita um jardim zoológico.
If a group of tourists visits a town, one can have the impression that they were visiting a zoo.
A história do uso de substâncias que melhoram o desempenho físico é mais antiga do que os jogos olímpicos.
The history of substances enhancing physical abilities is elder tan the olympic games.
A group of tourists is without article in English and Portuguese. In historia do (de + o) uso there is article in English and Portuguese.
de + noun as genitive
Quem abre a porta da casa é como quem abre o próprio coração.
Who oppens the door of his house, resembles to one who opens his heard.
Você já se perguntou para onde vai o dinheiro dos impostos?
Have you ever asked yourself where all this tax payers money goes?
To describe the origin de is used and in Portuguese the origin of a table made of wood is wood. In English it is of, made of wood, although from would be nice as well, given that it is the wood from sustainable supplies that we like most. In Portuguese it is from wood.
de to describe origin
Ela é de Lisboa*
He comes from
Rio de Janeiro
Ela é do Brasil.*
Ele é de Portugal.*
Ela é do Rio de Janeiro.*
Ele é da Bélgica.*
A mesa é de madeira.
The table is made of wood.
* Normally no article is used with names of cities. Rio de Janeiro is an exception. Name of countries in general have an article, Portugal is the exception.
If an action is triggered by something, for instance by an emotion, it is described with de as well in Portuguese. In English different prepostions are used in this case, to tremble with cold, to laugh in joy, to cry in pain, to die of fear, and perhap there is a logic, but the author didn't succeed to find one.
de in, with, of,
Meu cachorro morre de medo de fogos de artifício.
My dog almost die from fear of fireworks.
Multidões fora do hospital gritaram de dor quando o anúncio foi feito.
The crowd in front of the hospital cried in pain when it heard the news.
Muitas pessoas tremeram de frio.
Many people trembled from cold.
A lot of nouns can be connected to other nouns by the preposition de. It seems that the preposition used depends only on the noun and not of the grammatical function of the noun added. In the case of o desejo de João Romão we have a genitive, João Romão's wish, in the case of o desejo de riqueza, the desire to be rich, we have a preposistional phrase.
O desejo de João Romão de enriquecer determinará todas as suas atitudes ao longo do romance.
The wish of João Romão to become rich determines his attitude in the whole novel.
O desejo de riqueza é devido, na maioria dos casos, à ânsia de segurança.
The wish to become rich is in most cases due to the yearning of security.
Expression like the lack of, the need for, longing for requires the preposition de in Portuguese.
de of, for
Eu sei de quem é a culpa de tudo isto.
I know who is to blame for that.
A escassez de água é um problema cujos impactos são cada vez mais graves.
The lack of water is a problem whose consequences are more and more serious.
Os homens têm inveja de mim.
People are were envious of me.
Tinha saudade de tanta coisa.
I longed for so many things.
There are a lot of adverbials that contains de in Portuguese.
De noite todos os gatos fazem miau*.
By night the cats meowed.
De repente ficamos sem gasolina.
Suddenly we run out of gas.
De vez em quando eu saio com os amigos.
Sometimes I go out with my friends.
E isso os dirigentes não queriam de jeito nenhum.
That's what the responsables absolutly didn't want.
* a noite exists as well, but that means something different.
Todos os dias à noite, eu saio de casa. <=> I always go out, when it is dark.
If the main assertion is that something is repeated every night, it is a noite. If the main assertion is that it happens in the night, it is de noite. If the action happens only once, it is de noite.