184.108.40.206.1 First rule: Infinitive preposition = object preposition
The first rules for the different additions to a verb is, that the preposition used for connecting an infinitive is usually the same as the preposition that is used for connecting an object to the verb. As you will see, here we have a difference to English. Mostly the infinitives are connected with 'to' or no preposition and with an object there are many more possibilities.
Il parle de son enfant.
He talks about his child.
Il parle de s' acheter une nouvelle voiture.
He talks about buying a new car.
Il renonce à briller, il renonce à la gloire, il a compris que ce ne sont que des illusions.
He renounces to shine, he renounces the glory, he understood that they are only illusions.
Il aime manger de la confiture.
He likes to eat marmelade.
Il aime sa copine.
He likes his friend.
This again is a reason to repeat: just learn the verbs with their preposition and their type of object.