There are certain verbs that will always take de when followed by another verb. Some examples are essayer, rêver, and refuser.
So some sample sentences:
Elle essaye de venir. She is trying to come.
Elle rêve d’aller. She dreams of going.
Elle refuse d’écouter. She refuses to listen.
There’s really no rhyme or reason for what verbs take de, you just have to memorize them. Also remember that de is the article used with negation (il n’y a pas DE devoirs, etc.)