Most people use a campaign manager for generating an email list of followers. Mailchimp, Aweber, ConstantContact and GetResponse are such tools. Depending on the amount of people you have on your list you have to pay a monthly fee to these services, but they allow you to add a bit of code on your website where people can sign up to you. In a welcome email you can configure a link to a freebie – that’s how you can give something away when people sign up.
As for emails on your own domain, they usually work as a redirect. Assuming you already have an email address we can setup email@example.com so when people send an email there it will simply land in your current inbox.