If you do not already collect email addresses and opt-in status for emails on your app, see here to begin.
If you use MailChimp, Constant Contact, AWebber, or Zapier, you can automatically import data to your email subscriber list. Click here to find out how.
If you are already collecting this data, it is easy enough to get users added to a mailing list or newsletter. To do so, go to the Export -> Download Exports section of your campaign's dashboard.
Click the "Request Export" and then "Download Export" under Entries/Votes/Vouchers, etc. This will download a data file which can be opened in Excel, Google Docs, or any other spreadsheet application.
You will be looking for the field titled custom_#, where # is the number of the field type 'emailoptin'. To find this number, go to the Customize section of the offer, and click "edit" on the Form Fields component, then "custom mode."
In the code, it will say name= custom_#.
In this column on the spreadsheet, users who have this box checked will have a value of "on". You can then sort the sheet by this data to show all users in a row who have opted in. Depending on your program, you can then export all of those emails to be fed to the mailing list of your choice.