if you don't have a mailing list already, use the form block to make a simple form asking for an email and whatever other info you want. the data will be stored in the dashboard and you can export to CSV for your mailing app.

if you do have a mailing list already, it probably already has a signup form. You can add it to the content block while its in HTML mode if you want it to behave the same as it does now on submission, or you could play around with making it a custom form if you have a little php background.