The Diamond of Darkhold by Jeanne DuPrau

Months have passed since young Lina Mayfleet and Doon Harrow were forced to escape the dying subterranean city of Ember and flee to the town of Sparks, where they must struggle through a harsh above-ground winter. The situation seems hopeless until they chance upon a battered, fragmentary book that contains references to a device that could save them and their doomed city. To find that wondrous machine, the pair must descend to a realm where every hope seems but an echo.