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Por ejemplo:
Te voy a presentar a mi novia.
How can one tell whether this should be translated as
'I am going to introduce you to my girlfriend'
or
'I am going to introduce my girlfriend to you'
(This example is taken from Duolingo, where they side with the first translation)
It's not a matter of identifying direct or indirect objects. It's a matter of the right choice of the preposition.
"Te voy a presentar a mi novia" means "I am going to introduce my girlfriend to you"
If you want to invert the person that is being introduced, you use either con or ante (as Emilo Gort stated in his answer, the latter could sound old-fashioned. I agree, but to me it just sounds formal). Thus,
"Te voy a presentar { con or ante } mi novia" means "I am going to introduce you to my girlfriend"
Te is the Direct/Indirect Object Pronouns
Te => you
http://www.studyspanish.com/lessons/iodopro.htm
Update
You're right, the problem here is at least I use that phrase Te voy a presentar a mi novia. indistinctly for both cases. It depend of the context. I note English is more precise than Spanish.
If you want to be more precise to get I am going to introduce you to my girlfriend could be
Voy a presentarte ante mi novia
But this sound to me old fashioned
I am going to introduce you to my girlfriend
Voy a presentarte a ti a mi novia
I am going to introduce my girlfriend to you
Voy a presentarte mi novia a ti
But this is overkilled, and at least for me is not very common
OK, in Spanish if you say that sentence, there is not way people can be completely sure about the action. In both case, both of them will be meeting each other, so really is not that important, but... if you want to make things more clear, then Spanish is a very open language. I would prefer to use something like this:
(...to introduce my girlfriend to you) - Quiero que conozcas a mi novia - Vamos para que conozcas a mi novia
(...to introduce you to my girlfriend) - Quiero que mi novia te conozca - Vamos para que mi novia te conozca
There is no way to distinguish them in this case. Usually, whenever anyone uses that sentence, it may refer to: I am going to introduce my girlfriend to you.
In a way, both have a very similar meaning, so normally, when someone says it, they mean it as the second translation and everybody understands it that way.
It is possible to use that sentence as the first translation, but in general nobody would do that.
Altough both sentences mean the same, as in English, in Spanish we have many ways to say the things we want to say. Both sentences have accurate translations and both are right to say the exactly same thing.
'I am going to introduce you to my girlfriend' is for "(Yo) Voy a presentarte a mi enamorada"
and
'I am going to introduce my girlfriend to you' is for (Yo) te voy a presentar a mi enamorada.
Because in the first one you are saying that your girlfriend is the one that is going to know your friend, and in the second one you're saying that your friend is the one that is going to meet the girlfriend. As I said at the begining both mean the same but is just the form that you're saying it. Probably your girlfriend woul like to say that you're introducing the friend to her and not the other way, ha ha ha (at least mine would want that).
Another thing I would like to say is that the word novia actually means fiancèe or bride, not girlfriend, but it depends on the region, I know that in Argentina they usually says novias when they're talking about girlfriends. But, for example, here in Perú we call for enamorada, though it is not that accurate because it is not ascertainable that the girl you hang out with really loves you as the word suggest, but I think there's no translation for the word girlfriend, I think the ancient Spanish, who invented the words where more "love-believers" than English ones, just saying...
There is no real ambiguity. You introduce people to each other.
