There are several useful approaches for finding data.
Searching for data is a bit different than searching for books or articles, but it can be productive. However you'll need to do a slightly modified search. One useful technique is to use a site limiter to restrict your search to a particular kind of domain. Let's say you are looking for data on the voting turnout. Since professors and other academics are heavy users of data, you could focus and narrow your search to educational websites: .edu
Just type your search term into Google, and follow it with .edu site limiter syntax to restrict your search to educational sites: voting turnout data site:.edu
Alternatively, you could also use .gov to search for data on government sites.
Along with site limiters, you can also limit your search by file type. Since data sets tend to have particular kinds of file extensions (the three or four letters to the right of the period in a file name) you can use a Google "infile" command to limit your search to these file types. For example: voting turnout data infile:xlsx
This will limit your results only to Excel files. You could also use "xls" for older Excel files, "sav" for SPSS data sets, or "csv" for comma-delimited data. Other data extensions also can be used.
These kinds of data searches can turn up several different kinds of "hits." You may find specific data sets, or, alternatively, you may turn up resource websites like the site you are using right now.
To find resource websites, another useful technique is to look for LibGuides. A LibGuide is a library resource (this is actually a LibGuide). Just type LibGuide along with your search term: LibGuide voting turnout data
This will give you date-related LibGuides from other academic institutions. Typically, electronic resources will only be available to users from those libraries, but you will often get "Open Web" resources that you can use.
Working Backwards from Published Books or Articles
Another strategy is to try to locate published books and articles that use the kinds of data you need. If you are looking for data on voting turnout, try searching for books and articles on this subject, then see what kind of data they have used. If they cite a publicly available resource, you should be able to use it, or they may cite a data subscription service that UF subscribes to. In other cases, the data may have been gathered by the authors. In such situations, you can contact the author(s) of the paper to see if they would be willing to share their data with you. If the authors have been funded by a grant, they may be contractually required to share their data.
Another strategy is to brainstorm a bit about who might be likely to produce the kind of data you are looking for. Looking for data on voting turnout? Perhaps the Federal Election Commission would be a good source.