Someone else's project may have generated data you can reuse. Or a national/international organisation may have an established programme for collection and distribution of data relating to your research interests.
Gregory, Kathleen et al (2018) Eleven quick tips for finding research data. PLoS Computational Biology 14(4). https://doi.org/10.1371/journal.pcbi.1006038
An aggregated data catalogue for the Consortium of European Social Sciences Data Archives, containing over 20 000 records. Search by keyword and filter by year or country of origin. Not all datasets listed are available for re-use.
A searchable catalogue of datasets with a DOI (a stable digital ID) which have been harvested from repositories worldwide, including the UK's Digital Curation Centre, numerous scholarly societies and universities, plus self-deposit data repositories such as Dryad, Figshare and Mendeley Data. You can filter results by year, resource type (e.g. image, software) or researcher's affiliation.
A search engine to enable the discovery of data from multiple member repositories in the Earth and environmental sciences, mostly based in Europe and the USA.
Search the EDS Data Catalogue, or browse (by topic or region) for over 10 000 datasets and maps with an open licence, deposited by environmental scientists working in the UK and around the world.
"Similar to how Google Scholar works, Dataset Search lets you find datasets wherever they’re hosted, whether it’s a publisher's site, a digital library, or an author's personal web page".
Note that to be indexed in Google's Dataset Search, the data provider needs to adopt Google's own schema for describing their content, which means search results will not necessarily be a complete picture of all relevant web content. Non-visibility of known datasets in search results should not be taken as any indicator of quality or otherwise.
See the University of Hull's guide to Statistics collections, including subscribed economic, financial and marketing databases, plus free-to-access authoritative sources:
The Library's guide to citation styles includes examples of datasets and printed volumes of data in Harvard, Footnote, OSCOLA and APA formats.