1. Create a dynamic query for the appropriate record type and filter by Date Last Changed equals Today (or the operator appropriate operator).
    For example, if looking for gifts, run a Gift Query; if looking at Constituents, run a Constituent Query, etc.
     
  2. Create an export of the same type and use the query created in step 1. Export the appropriate information such as Date Last Changed, Last Changed By, etc. Run the export on a daily basis (or as needed).