Translation:The girl looked out the window but saw nothing.
But for future reference, there is a slight difference between the two, being that "into" implies motion to the inside, while "in" implies a state. Compare "She jumped in the room." and "She jumped into the room." For looking though a window though, the difference is not relevant, as you cannot be physically inside the window.
I guess there is no such information in the Russian sentence but more often there is implying of looking out the window from inside towards the outside if there no any context. Although if we look at "out" in the English sentence we can conclude that it implies looking out the window from inside towards the outside. Sorry for my bad English.
In English, you look into something - a room, a box, a possibility. You look in a window or through a window. This is a minor point of grammar and meaning. You can look in a mirror or 'looking glass' (old fashioned). https://en.wikipedia.org/wiki/Through_the_Looking-Glass - Alice goes through the mirror. This book by Lewis Carroll contains a famous nonsense poem 'Jabberwocky' which I believe has been translated into Russian as БАРМАГЛОТ.
I initially made FabioPratz's mistake too, but quickly realized what Kundoo is saying. Perfective verbs imply a discreet action, like "looked" and not a continuous (imperfective) action/condition like "was looking." Kudos to Kundoo for an excellent point that we all need to be picking up at just this stage!
I think "in the window" is probably the most common way I've heard this (in the US). "through the window" is fine, but might imply the view is not easy somehow; there's a glare or the window is up high or something, because otherwise it's obvious you're looking through it. You don't NEED to specify "through". "Into the window" is fine too but again possibly suggestive of an unusual situation. Its use is less common so you might reserve it for indicating something special, like, 'hint, hint, there is something unexpected in there, look more closely'.
"Девушка" mostly means "young woman", or "girl from her late teens to thirty something". The word gains the additional meaning of "girlfriend' only when used with a possessive, just as bsalinasz13 said. In this sentence "girlfriend" would be an incorrect translation.
"Девочка" is a little girl or a young teenager.
I see. I suppose it depends on context, too?
How about giving the situation some different context, could one say something like this?
Он, его девушка и его сестра вошли в дом. Девушка посмотрела в окно а ничего не увидела, но сестра увидела что-нибудь..
Here you would have to say девушка, as using она would leave it ambiguous as to who did look through the window. Would those sentences sound natural in Russian, or would you really have to use a possessive once again on the second sentence? In English you'd have to repeat the possessive, but in Portuguese you shouldn't:
Ele, sua namorada e sua irmã entraram na casa. A namorada olhou pela janela e não viu nada, mas a irmã viu algo.
I think, you would be understood if you leave the possesive out, but it's better to use it.
Of course, since you already established that you use the word "девушка" in regard to the second person mentioned in the first sentence, we would automatically assume that in the second sentence this word applies to the same person. But it does sound slightly off, if you ask me. I don't think that would work if you keep using "девушка" without the possesive throughout the whole text, unless you also tell at some point that the sister is too old or too young to be called "девушка".