In order to download the responses to TeamRaiser registration survey questions, you will need to build a custom TeamRaiser report in Report Writer.  Follow the steps below to build this report:
  1. Data Management > Reports
  2. Click Report Writer
  3. Click Create a New Report
  4. From the Select Application drop-down, select TeamRaiser
  5. From the Available Reports list of options, select Registration
  6. In the Select Columns step, be sure to mark the box for Survey Questions located in the Survey Information Section. (you can find this by hitting ctrl+f and then typing in Survey Question)
  7. Go to Step 5. Configure Filters and make sure you have the Event you are wanting to report on specified in the filter
  8. Label the Report
  9. Click Run or Save Report
  10. Follow the prompts into you reach the last step.  Click on Run Report 
  11. Once the report finishes running, you will have the option to download it to a CSV file by clicking on the floppy disk icon located on the upper left hand side
Please note that questions created as Unlimited Text Value question types will be excluded from the report.  You can still view individual responses to these questions through the interaction tab of the constituent record.