Define the specific elements of your question: time, geography and subject matter.
Include methodological terms to search for data obtained by particular tests or procedures, e.g., Beck Depression Inventory II; fMRI; EEG; eye-tracking; etc. Be aware, though, that researchers may not use terms this specific in study abstracts.
Consider what organizations might pay for data collection on your topic.
government (international, national, state, local...)
academe (directly from a researcher or indirectly from a repository)
Read the literature for possible sources, but beware that sources noted in articles may not be openly available.
Will data be costly in terms of money or time to obtain? Do you have the requisite knowledge to manipulate it?
You may not be able to find exactly what you'd like. Be prepared to be flexible on one or more of your question elements.
Read the technical documentation!
Consider the purpose for which data were collected, and their limitations.
Ask the experts (both about finding and understanding data).