Run is a custom website builder platform and you can not automatically transfer an existing site design or files directly to Run. You will have to build a new site on Run, or pay Run to build it for you.
However, the process is very simple:
Building the site on Run is the first part, and we recommend you watch our demo video get a sense of how easy that is.
Once the site is built and paid for, all you need to do is to change two DNS records on your domain account and you'll be live on Run with a few minutes.
A few important notes:
We recommend you continue to host your domain wherever it was already. If your domain was on Squarespace, for example, keep hosting it on Squarespace. If your domain was on Godaddy, keep it there. Run does not sell or host domains.
You will probably want to cancel your old website hosting account, even as you continue paying for domain hosting. If your domain and web hosting are in different places, you can fully cancel or delete the account at your web host.
Your email will continue to work without interruption. Your email server is determined by "MX" DNS records, and those won't change. So, if you host your email on Google currently, you'll continue hosting it on Google.