The conditional is used to express a possibility.
To make assumptions (usually in constructions with “if”)
Exemple:
Si tu n’avais pas téléphoné je ne serais pas venue.
To give unconfirmed information
Exemple:
L’accident aurait fait 15 morts
To express a desire or a wish
Exemple:
Je voudrais devenir bilingue en français.
or in the past tense to express regrets or missed opportunities
Exemple:
J’aurais voulu être un artiste.
The conditional tense can be used to express politeness or to order something in a café:
Exemple:
Je voudrais 2 pains aux chocolat, s’il vous plaît.
Formation of conditional in French
In the present tense: the present conditional is formed by using the future tense base (the radical) and the imperfect tense endings.
Verb (future tense) + imperfect endings
Exemple:
Manger (je) – Manger + ais – Je mangerais
Vouloir (je) – Voudr + ais – Je voudrais
Past conditional in French
Past tense: the past conditional is a compound tense that is formed with “to be” or “to have” in the conditional and the past participle.
To be/have (present conditional) + past participle
Exemple:
Manger (je) – J‘aurais mangé du gâteau si je n’étais pas au régime.
Venir (je) – Je serais venu si tu m’avais appelé.
To go further and boost your French I recommend you check my video course, or if you want a personalized approach, or want to practice conversation contact me for a private lesson.
Ressources: https://grammar.collinsdictionary.com/french-easy-learning/how-do-you-form-the-conditional-in-french