To cut to the chase, I have an arbitrary Heroku domain that I'd like to transfer to a custom domain. I've never done this before. I've looked into it but haven't found a clear enough answer broken up into steps.
1) Buy a domain from a domain-registrar (godaddy.com, networksolutions.com)
2) Add the domain to your heroku app => heroku domains:add
3) You'll see an option to alter DNS records on your domain service provider's account dashboard, add a "www" C-Name DNS record and point it to your heroku app (e.g. yourapp.herokuapp.com)