How does Yuuki talk like a boy?
In Japanese, there are multiple words for "I", the most common being watashi, atashi, boku, and ore (I'll transliterate to romaji thoughout). Most of these pronouns are definitively gendered, and it would be quite the social faux pas to use an improperly gendered pronoun. This video does an excellent job explaining the subject.

From S02E19 Zekken


  Yuuki: Boku wa kore dake, dakedo ne.
  
  Translation: I'll just use this, though.


In SAO, Yuuki uses boku.

Boku is generally a male pronoun. However, in anime (not so often in real life) excessively tomboy type girls will use boku in an attempt to sound masculine. This is something that is generally impossible to accurately translate into English in an acceptable way, so most official translations simply ignore the distinction, but most fansub groups will add a translator's note demarking this.