Are you looking for data or statistics? (See about data and statistics.)
Do the data or statistics exist? Most of what happens is not recorded. What is recorded often is not recorded consistently over time or in different places. When data are recorded, it's usually because it is valuable, worth the time and effort to record, and thus may not be available for free. Or, access may be restricted to protect confidentiality.
Who would collect these data or produce these statistics? If you can think of some possible collectors of relevant data, check their websites to see what they provide, or contact them directly. For some examples:
What data sources have others used? Find academic articles on your topic of interest that present statistics or use data analysis and see what data sources they used (search for "[topic] and data"). Usually you can find a list of data sources in the early part of an article, either in the Introduction or Methods section.
Data and statistics sources Wesleyan Library subscribes to. Check the brief descriptions to see if any are likely to have data or statistics you are looking for.
Google's Dataset Search locates online sources of data and statistics, most are at least partly freely accessible, though many charge a fee for full access.
Search the Internet using your favorite search engine. Try searching for "[topic] and data" or "[topic] and statistics." Always check the source of the statistics or dataset to verify the reliability of what you find.
Find statistics to find data. If you are looking for a dataset for a topic and find a relevant statistical chart or graph on a website or in a book or article, see if the data source from which the statistics were derived is noted. Try searching for "[topic] and statistics" or look in a statistical compendium such as Statistical Abstract of the United States.
Combine datasets. The data you need to answer your question may be in different datasets. If so, see if you can find a way to connect them (e.g., an overlapping variable). This may take some creativity, or may not be possible.
Adjust your research question. You may not be able to find the data you need to answer your research question. But if you find related data, you can ask an interesting question you can answer with the data you have.