How to explain emoticons to an autistic person?
First question, how deep is your knowledge about autism and Asperger Syndrome? Do you understand how autistic people think? Do you understand, what this girl have meant, when she have written, she doesn't really understand what each means?

For neurotypical person, a typical use-case for I understand you phrase is I know what you feel. But autistic people by understand mean in the first line to know the cause-and-effect. So your friend saying she don't understand what really each emotion means, could as good mean: I don't know how particular emotions are affecting the meaning of words the given person use. 

If you want to explain emoticons to her, you should IMHO in first line explain, how particular emoticon in modifying the meaning of the sentence. So, think of emiticons not as the way to communicate emotions (which is of low importance to autistic people) but as the modifiers that change the meaning of the sentence or of the particular words.