"Sign up" button or link placed in an email message
The "Sign Up" button that you find in some of the customizable templates in the console allows non-subscribers to whom the message has has been forwarded to subscribe to the newsletter.
Note that such a message should never be used to acquire new subscribers. One thing is an existing subscriber forwarding the message to a friend, who might then decide to subscribe as well. In that case the message becomes a private message between two parties that know each other. A whole different thing is for you to send such a message to N recipients that are not subscribers. That's SPAM, as you would be sending a message unsolicited, even if you believe that the recipients might have an interest in signing up for the newsletter. Never send unsolicited message: it will just hurt your reputation (and it's against the Terms and Conditions of Use of this service).
Once again, the only purpose of a "Sign Up" or "Subscribe" button/link is to allow people to subscribe to the newsletter when and only when the message is forwarded by subscribers to their contacts.
The new subscriber will need to submit their information via a subscription form that the button/text link will point to. You can place the subscription form on your Web site, or have it hosted by the system. There are over 25 subscription forms to choose from under Settings -> Registration form. Note that this feature must be enabled: just go to Settings -> Edit Lists -> Show advanced options, find "Frontend form", and select "Yes".
To link to a form from an email, select the image or text link (e.g. the "Sign Up" button that might already exist in the message template), and associate it with the URL of the subscription form, using the "Insert Link" button in the  editor. Enter the link to the form, either taken from your site or from the administration console depending on whether the sign up form is hosted by you or by the system.