Think about who or what organization might collect the data you are interested in. Visit their website to see if they make data available.
government agencies
nonprofit organizations
business/industry organizations or corporations
universities or academic research institutions
Include search terms like "raw data", "raw datasets", "unaggregated data"
Search example: criminal justice unaggregated data
Search example: water pollution raw dataset
Search for a particular document or file type. Often datasets are found in excel sheets (.xls) or other similar document types such as .xml, .csu, and json. Use the document type in your search.
Search example: json AND climate raw dataset
Also, try the Advanced Google Search and use the file type field to select a specific type of document.