To build a form into a Next.js website without setting up a backend, you can use Netlify Forms. This involves creating a contact page component with a form and adding a `data-netlify` attribute to the form tag. You also need to create a success page that will be displayed after the form is submitted successfully. The form submissions can be verified in the Netlify dashboard, and there are additional features such as spam prevention and serverless functions available for customization.