Organic semiconductors show promise to yield a novel class of bendable electronic devices, and much research efforts have focused on the optimization of these films for device performance. It is well known that the structure of organic films has a large influence over the electronic properties. In particular, the carrier mobility is often highly anisotropic, and domain boundaries have a detrimental effect on charge transport. Therefore the domain structure and lattice orientation are of particular interest. However, little is known about the domain structure of organic films, and techniques to study these properties have only begun to emerge in recent years. In this thesis, we apply two experimental techniques, Grazing-Incidence X-ray Diffraction (GIXD) and Lateral Force Microscopy (LFM), toward studying the lattice and domain structure of tetracene films grown on the silicon(001)-monohydride surface. We describe the necessary steps toward optimizing the sensitivity of these techniques to the domain structure. Results show that the crystalline tetracene films form a layered morphology in which the a-b plane lies parallel to the substrate surface. The film lattice structure is similar to bulk tetracene, and the lattice is confined to two orthogonal orientations, forming a partially-commensurate relationship with the substrate surface lattice along the film 'a' axis. LFM images reveal two types of polycrystalline domains. The first type ("major domains") are tens of microns in size, and are classified by their lattice orientation. They are subdivided into the second type ("sub-domains"), which range from 0.1 to 5um in size, and are argued to represent regions of uniform molecular tilt direction. The GIXD data show that the single-crystal domains which comprise these two larger domain types are anisotropic in size, being up to two times longer along the film 'b' axis than along 'a'. The single-crystal domains range from 0.05 to 0.2um in size, depending on lattice orientation and film thickness. The mathematical basis for these single-crystal domain size calculations is presented. The single-crystal domain sizes are thickness-dependent, and are two orders of magnitude smaller than a typical surface island observed in atomic-force microscopy (AFM) topographs. Substrate steps can also significantly influence the film structure by inducing boundaries in the single-crystal domains and sub-domains, but not in the major domains. This detailed knowledge of the domain structure of organic thin-films may assist in our understanding of the factors which affect charge transport in thin films, and may help to direct research efforts in optimizing the film structure for device performance. / Natural Sciences and Engineering Research Council (NSERC), Canadian Foundation for Innovation (CFI), Ontario Innovation Trust (OIT).