We do not have at present any direct personnel grants or studentships, but the Consejo Superior de Investigaciones Científicas (CSIC) offers several research training programs that may fit your academic level. The Departamento de Posgrado y Especialización del CSIC has published a good overview of those programs:
The world of research grants and studentships offered by different administrations (european, national, regional) and private foundations is too wide and dynamic to summarize it (and to keep the summary updated) here. The FECYT has a couple of brochures that could be a good starting point: