The physical properties of materials are dominated by their structure and composition. Insight into the structure of complex oxide materials has the potential to improve our understanding and eventually control of their physical properties. This PhD thesis reports the development of characterization and fabrication techniques relevant to improving the scientific understanding of complex oxide materials. The work presented here has two components. I report a way to use ideas that were originally developed in semiconductor processing to control the elastic strain state and crystallization process of the model complex oxide SrTiO3. An additional component is an important series of advances in the analysis of diffraction patterns acquired with focused x-ray nanobeams. The fabrication and characterization of nanoscale SrTiO3 has been experimentally shown to allow the introduction of elastic strain into SrTiO3. The creation of thin SrTiO3 crystals from (001)-oriented SrTiO3 bulk single crystals using focused ion beam milling techniques yields sheets with submicron thickness and arbitrary orientation within the (001) plane. Synchrotron x-ray nanodiffraction experiments show that the SrTiO3 sheets have rocking curves with angular widths less than 0.02°. These widths are less than a factor of two larger than bulk SrTiO3, which shows that the sheets are suitable substrates for epitaxial thin film growth. A precisely selected elastic strain can be introduced into the SrTiO3 sheets using a silicon nitride stressor layer. Synchrotron x-ray nanodiffraction studies show that the strain introduced in the SrTiO3 sheets is on the order of 10-4, matching the predictions of an elastic model. This approach to elastic strain sharing in complex oxides allows the strain to be selected within a wide and continuous range of values, an effect not achievable in heteroepitaxy on rigid substrates. An additional fabrication technique is also evaluated here based on the crystallization of SrTiO3 from initially amorphous thin films. This process is known as solid-phase epitaxy in two-dimensional samples but is just beginning to be explored in more complex geometries. I report experiments in both homoepitaxy and heteroepitaxy including measurements of crystal growth rates and the crystallographic orientations of crystals formed in this way. The lateral growth rates are consistent with previously measured vertical growth. This result indicated that previous work on vertical solid-phase epitaxy could be extended into lateral solid-phase epitaxy, which has the power to be applied to complicated non-planar geometries. The highly coherent and tightly focused x-ray beams produced by hard x-ray light sources enable the nanoscale structural characterization of materials but are accompanied by significant challenges in the interpretation of diffraction and scattering patterns. I report here a series of methods that expand the range of physical problems that can be accurately captured by coherent x-ray optical simulations. My approach has been to expand simulations methods to include arbitrary x-ray incident angles and arbitrary epitaxial heterostructures. I first applied these methods to extract the misorientation of lattice planes and the strain of individual layers of Si/SiGe heterostructures relevant to applications in quantum electronics. Further applications reported in this thesis are in probing defects created in the processing of SrTiO3 and in measuring the change in lattice parameter introduced into strained SrTiO3 sheets. The systematic interpretation of nanobeam diffraction patterns aids in the fabrication of SrTiO3 nanostructures.