We are an organization that has donors ("constituents") and potential donors (also referred to as "constituents"). We would like to run a query that identifies potential donors--i.e. "constituents" who have never made a donation. How would we do this?
Create a group of your donors, and then run a Custom Search of Include/Exclude.
One option is to create a group (preferably a smart group) using "Advanced Search" or "Find Contributions": the only search condition is a Contribution Status of Completed. This will put all of your donors into a group (if you use a smart group, the group will continually be updated).
Then use a Custom Search that comes with CiviCRM - Include/Exclude. Do a search that EXCLUDES the group of donors you just created. You now have your constituents who have not yet donated.
Additional: From that Excludes custom search, you could then create another smart group -- this time, it would be a smart group of those people who haven't donated.