How does one construct a sentence containing "to teach someone something"? Can I have two objects in the accusative or do I need a preposition?
Which is correct?
Using two direct objects with one verb is not recommended; I'm not sure if it's technically ungrammatical, or just strongly unpreferred, but in either case it's best to avoid sentences like *"Ŝi instruis lin la francan".
The other two options are both acceptable, and I have seen both used frequently. Either the student or the subject taught can be the object of instrui, and the other, if mentioned, is introduced by the suitable preposition, I can instrui ion al iu or instrui iun pri io. There may be a difference of nuance: if I instrui al li la francan that implies that I'm teaching him to speak and understand French, that French is added to his knowledge. Whereas if I instrui lin pri la franca, then perhaps I'm just teaching him about its grammar and vocabulary, or perhaps its history and literature, but not necessarily to speak and understand it. (instrui al li pri la franca has essentially the same meaning).
If only one object is mentioned, then of course context and feasibility determine the meaning. But of course one can imagine an interchange like "Mi instruas la anglan." "Bone, la angla ja bezonas ion lerni!" But obviously that's a joke, not an actual misunderstanding.
You will see it both ways. In most cases, you use instrui with al:
However, it is possible for the learner to be the direct object (examples from Fratoj Grimm and La Malnova Testameno:
Cases where the object of instrui is a pronoun are very common. Here's just one from Fundamenta Krestomatio de la Lingvo Esperanto
Similar examples of the form instrui iun pri are common throughout the Esperanto literature.
If you're teaching an action, the subject is accusative.
Mi instruis lin paroli france.
If you're teaching something where the accusative on a noun is appropriate, use instrui al ~.
Ŝi instruis al li la francan.
