The short (pun) answer is she was small.
The long answer is a series of lucky circumstances left Newt the lone survivor of the alien infestation.
This is from JamesCameronOnline.com:
The entire colony was enormous in size, with multiple large complexes connected together. And as seen in the movie, aliens retreated to the hive deserting the entire place. Newt played with other kids hiding in the vents before the colony became infested and she was the best in fitting in tight spots. That's why she got called Newt. That's how she survived the initial attack by going into small places no one else could fit and then when the alien warriors deserted the place and retreated into the hive under the heat exchanger, she moved around through the vent tunnels. By that point the place was relatively safe since aliens lied dormant in their hives.
Her age also probably helped since she would have been considered too young to assist with the defense of Hadley's Hope.
Newt's gender may have also helped. While Newt's brother, Tim may have had the size requirements to fit in the hiding places Newt used, he may have felt the need to defend his sister causing his death.
Newt's interests may have also helped. In her introductory scene she expresses her interest in mazes:
NEWT "Daddy, when are we going back to town?"
JORDEN "When we get rich, Newt."
NEWT "You always say that. I wanna go back. I wanna play 'Monster Maze.'"
TIM "You cheat too much."
NEWT "Do not. I'm just the best."