This thesis utilizes new observations of dense gas in molecular clouds to develop an empirical framework for how clouds form structures which evolve into young cores and stars. Previous observations show the general turbulent and hierarchical nature of clouds. However, current understanding of the star formation pathway is limited by existing data that do not combine angular resolution needed to resolve individual cores with area coverage required to capture entire star-forming regions and with tracers that can resolve gas motions.

The original contributions of this thesis to astrophysical research are the creation and analysis of the largest-area high-angular-resolution maps of dense gas in molecular clouds to-date, and the development of a non-binary dendrogram algorithm to quantify

the hierarchical nature and three-dimensional morphology of cloud structure.

I first describe the CARMA Large Area Star Formation Survey, which provides spectrally imaged \NtwoH{}, \HCO{}, and HCN ($J=1\rightarrow0$) emission across diverse regions of the Perseus and Serpens Molecular Clouds. I then present a detailed analysis of the

Barnard~1 and L1451 regions in Perseus. A non-binary dendrogram analysis of Barnard~1 \NtwoH{} emission and all L1451 emission shows that the most hierarchically complex gas corresponds with sub-regions actively forming young stars. I estimate the typical depth of

molecular emission in each region using the spatial and kinematic properties of dendrogram-identified structures. Barnard~1 appears to be a sheet-like region at the largest scales with filamentary substructure, while the L1451 region is composed of more spatially distinct ellipsoidal structures.

I then do a uniform comparison of the hierarchical structure and young stellar content of all five regions. The more evolved regions with the most young stellar objects (YSOs) and strongest emission have formed the most hierarchical levels. However, all regions show similar mean branching properties at each level, suggesting that dense gas fragmentation proceeds in a hierarchically similar way from earlier to later stages of star formation. Compared to the more evolved YSOs, the youngest YSOs are preferentially forming within leaves and at high-level locations in dendrogram hierarchies, indicating that dense gas in molecular clouds must reach a state of hierarchical complexity before young stars form efficiently.