In the Project Editor's "Deploy" panel, you'll be able to enter the domain you wish to use. After you've entered the custom domain you'll be provided with the A Records to add to your domain's DNS records.
Here's a quick video explaining:
Updating Your Domain's DNS Records
All custom domains pointing to a deployed CodePen Project will need to use the following A records.
|A||(your domain name)||184.108.40.206|
|A||(your domain name)||220.127.116.11|
You'll need to update these records via your domain provider. If there is any existing A records, you should also remove those. These are usually editable under 'DNS' or 'DNS Settings' in your provider's domain settings. The following are specific instructions for the more common domain providers.
If your provider isn't in the list above or you're still not sure how to update your A records, contact your domain provider to get assistance.