"Elle est montée à l'étage."
How does 'to the second floor' make any sense here, since there is no mentioning of any numbers?
I think this is because the first floor is typically called the "rez du chaussee" and so the by the time you get to using "etage" you are on the second floor?
Not really, this is an issue on their part. Since you could say "je vais à l'étage prochain" from the "rez de chaussé", saying you are going to the 1st floor (usually 2nd floor in North America).