The correct term is 'pilotar' or 'pilotear'(in some regions), so the sentence should be: ¿Quieres aprender a pilotar un avión? However, I don't agree with alezzzix when he says that not everybody would be familiar with 'volar un avion', In fact, it is a very common Spanish idiom.
It depends on what verb is being used. As described in the Tips and Notes for this section,
certain verbs, such as aprender, ayudar, and empezar, require a before the infinitive.
Note that, as stated by Jim226018 elsewhere in this discussion,
the tip is intended to show that the 'a' is after the affected verb and before the infinitive that follows.