The last way you want to add email addresses to a list is by just collecting them from here and there. It's best if people opt-in or at least have done some business with you or your company recently. Make email address collection a course of every transaction or conversation. Of course, you always must include an unsubscribe link (it's the law) in each and every mailing you send so people have the opportunity to have their email address removed from the list.
Blogging is one of the best ways to get interested readers to add their names to your mailing list. Discuss the details of how your product can benefit your readers and how it has helped someone specifically. Also if you have something to give away like a resource guide, you can offer that when someone signs up for your mailing list.