Run is a website service only and we don't manage or assist in your campaign's email setup. That said, we do get asked about it a lot, so here's a brief primer.
The most commonly used email provider is Google, and it can be used to host email accounts with your custom domain. However, there are thousands of email hosts to choose from.
In order to use email with your custom domain name, you'll need to create your email accounts on the email host and then set up your DNS records to tell the internet where your email is hosted. DNS records are usually (though not always) hosted where your domain is hosted, and the DNS records related to email are called MX records.
On the other hand, the DNS records that relate to your web site are A records and CNAME records (the latter is for subdomains, like www).
So you'll have MX records that point to your email host, and A and CNAME records that point to your Run website.