To gain more email addresses, you could create valuable online content, such as an eBook or a regular blog. Write on topics you can talk about engagingly and with authority, and which customers and prospects would find useful. Invite people to subscribe to your blog or submit their email addresses to download the eBook.
Most importantly, anything you email to people should be relevant and valuable to them in some way.
Giveaways and competitions with the right terms and conditions can be a good way to promote your business and build your email list. Think about offering a prize for joining your mailing list and announce the winner to all subscribers.