From what I can gather, this has the same scentence structure French does, without all of the words. (The house of my friend vs. My friend's house) They just say "She student my friend". I guess of you look at it and see that this is what the sentence portrays you can work it out?
Possession in Russian is expressed through the genitive case -- моего друга is genitive, so this sentence is absolutely unambiguous. You can look at it in opposition to, for example, "He's my [female] student's friend" --> Он друг моей ученицы. You're not entirely wrong in your comparison to French, as the genitive case here fills the same role as the preposition "de" does in "C'est l'ami de mon élève." -- you simply were missing a crucial bit of information :-)
Of course kpagcha's proposed translation is also correct, and it's almost certainly been added to the possible answers by the mods since then.
Свой and its declensions always refer to the subject of the sentence as the possesser (the subject is the noun or the pronoun in the nominative case), so here «Она ученица своего друга.» would mean "She is her [own] friend's teacher."
It's also true when you or I are the subject of the sentence, and this is where it gets hairy for us English speakers. For example, "I am my brother's keeper." in Russian becomes «Я хранитель своего брата.» and not «Я хранитель моего брата.» Likewise, "Mind your own business." becomes «Занимайся своим делом.» and not «Занимайся твоим делом.»
@JasonHave, use свой in situations like:
I see my brother
You see your brother
She sees her brother
We see our brother
They see their brother
So the the first word in the sentence, and the possessing word later on refer to the same person(s). Therefore you can't use свой in cases like:
I see your brother
They see his brother
She sees our brother
Definitely. To get the Russian sentence order right, convert an English sentence with a 's suffix word to a sentence using "of" (She is my friend's student => She is the student of my friend). English marks the genitive by putting "of" in front the word. So you can see the languages are very similar.