You should have a sign-up form on your website or blog, and ask for visitors to sign up for your free ezine, weekly tips, or whatever you send to keep in touch with your prospects and customers.
Make it easy for people to sign up. And if you use a professional service like Aweber, the process is pretty automated for you too.
Many sites use a “pop-over”, to force visitors to either enter their email address or close the box. This is something that you will want to test to see if conversion rates are better. It will depend on the market and perhaps on the layout of your site.
Another technique you can use is encouraging your readers to forward your email to friends or colleagues who would enjoy it. Some of them may sign up for your list.
A similar technique employed by some websites is a feature whereby one can send an article, or a link to it, directly from the website to a friend or colleague. Again, this technique should result in more readers added to your list.