In an ideal world there would be a meta search engine for finding previously created data - but no such tool currently exists.
For now, there are different places and ways for storing datasets. Datasets can be found in publication supplements, in separate data publications, in subject specific repositories or in general-purpose repositories like Zenodo, Figshare or OSF.
Stirling researchers are asked to deposit their research datasets in DataSTORRE (note some funders also require you to make your data public or cite where your underlying data from publications can be accessed). See the DataSTORRE deposit guide.
Your dataset will be given a unique, persistent URL that you can use to cite your data in publications and on web sites.