Searching for datasets may superficially resemble searching for articles or other text information sources, but there are important differences to consider. The goal is to find datasets that can be used to answer your research questions, which means the dataset must contain variables relevant to your hypothesis. Different sources of data may or may not define variables the same way. Studies may have dozens or hundreds of variables, not all of which will be discussed in a study description or abstract, so you will either need to use search systems that can search variables or examine data documentation defining the variables. The dataset may not exactly match the way you'd like to operationalize your variables, so you may need to tune your hypotheses to the available data.
Many data repositories exist to hold datasets, including those from governmental and non-governmental organizations, international organizations, and academic and research institutions.
Chapman has its own research data repository: Chapman Figshare
Datasets can be categorized by subject areas. In the Data Sets and Resources tab on the left, you can find numerous repositories specializing in specific domains.