To add a form to your checkout process to ask customers how they found your site, you can login to your admin panel and go to Cart Settings > Forms Control / Custom Fields.
This section will allow you to create any one of the following user inputs:
Text Box
Drop-Down
Radio Button
Text Area
Check Box
If you looking to collect referral information, I would suggest using a Drop-Down.
Simply go to this page, select Create A Custom Field, select where you want the field to appear and enter the Field Type as Drop-Down. You will be able to enter in the data for the drop-down box in the field below. Once you are done, click Save Changes.
