Here are some examples:
* J'ai peur du noir. (I am afraid of the dark.)
* Il a peur des araignées. (He is afraid of spiders.)
* Elle a peur de parler en public. (She is afraid of public speaking.)
You can also use the verb "avoir peur" (to be afraid) followed by "de" + the object of your fear:
* J'ai peur de l'avion. (I am afraid of flying.)
* Il a peur de se faire mal. (He is afraid of getting hurt.)
* Elle a peur de perdre son travail. (She is afraid of losing her job.)
For more informal situations, you can use "avoir la trouille" which is a slang expression meaning "to be scared."
* J'ai la trouille de me perdre dans la forêt. (I'm scared of getting lost in the forest.)
* Il a la trouille de l'orage. (He is scared of the thunderstorm.)