Subject Pronoun
Three forms in English (that, who, which) --> one form in French (qui)
that
I need to find a taxi that could drive me to the airport.
Il faut que je trouve un taxi qui puisse me conduire à l'aéroport.
who
The neighbour's son, who is always crying usually, has been strangely quiet today.
Le fils du voisin, qui est toujours en train de pleurer d'habitude, est étrangement calme aujourd'hui.
which
The Eiffel tower, which was built for the world exhibition in 1889, has become one of the most famous monuments in Paris.
La tour Eiffel, qui fut construite pour l'exposition universelle de 1889, est devenue l'un des plus célèbres monuments de Paris.
Object Pronoun
Four forms in English (that, whom, which or elision) --> 1 form in French (que, but note that que becomes qu' when used before a vowel - see examples below)
that/0
The house that my parents want to buy is very big/
The house my parents want to buy is very big.
La maison que mes parents veulent acheter est très grande.
Note that you always need to use the relative pronoun in French even when it is not used in English, that's why the two English sentences above translate into only one sentence in French.
The house that they want to buy is very big/
The house they want to buy is very big.
La maison qu'ils veulent acheter est très grande.
Observe the elision of the 'e' when the pronoun comes before a vowel. Here the pronoun is followed by 'ils' beginning with the vowel 'i'. Therefore the 'e' in 'que' is elided, giving the form qu'ils and not que ils.
whom
Professor Dupont, whom I met yesterday, is very knowledgeable in his field.
Le professeur Dupont, que j'ai rencontré hier, est très savant dans son domaine.
which
The mushroom which he ate was poisonous.
Le champignon qu'il a mangé était vénéneux.
Indirect Object Pronoun
In English the sentence using an indirect object relative pronoun can be built in two ways:
1.Marc is the only person I can get along with.
2.Marc is the only person, with whom I can get along.
but in French only the second sentence structure shown above can be used, as follows:
2.Marc is the only person, with whom I can get along.
Marc est la seule personne avec qui je peux m'entendre.
I think the candidate I voted for is going to win the election.
(but the French say...) I think the candidate for whom I voted is going to win the election.
Je pense que le candidat pour qui j'ai voté va gagner les élections.
The man she is smiling at is her husband.
(but the French say...) The man at whom she is smiling is her husband.
L'homme à qui elle sourit est son mari.
The company I work for is going to merge with a competitor.
(but the French say...) The company for which I work is going to merge with a competitor.
L'entreprise pour laquelle je travaille va fusionner avec un concurrent.
The book which this article refers to was written by Professor Dupont.
(but the French say...) The book to which this article refers was written by Professor Dupont.
Le livre auquel cet article se réfère a été écrit par le Professeur Dupont.
(auquel is the contraction of à lequel)
Genitive Pronoun
Two forms in English (whose, of which) --> one form in French (dont)
The Martin family, whose son is always crying usually, has gone on holiday.
La famille Martin, dont le fils est toujours en train de pleurer d'habitude, est partie en vacances.
Note that we are talking about the Martin family's son, le fils de la famille Martin. The preposition de here indicates belonging or ownership, and in a relative clause, the relative pronoun used to express those notions is dont.
So, whenever the relation between the antecedent of the relative clause (like 'la famille Martin') and the subject of the relative clause ('le fils') could be expressed by de in a normal sentence, think of using the relative pronoun dont.
See another example below:
Professor Dupont, whose ideas and findings are groundbreaking, is very famous in the academic sector.
Le professeur Dupont, dont les idées et découvertes sont révolutionnaires, est très célèbre dans le milieu de la recherche.
Again, as seen in the previous example, note that we are talking about Professeur Dupont's ideas and findings, les idées et découvertes du Professeur Dupont. Since the preposition de is involved (du is the contraction of de le), we use the relative pronoun dont.