Personally, I would just use an email to request a newsletter subscription,
but if you want a form then reference: Publisher web publication forms 101:
http://msmvps.com/blogs/dbartosik/archive/2006/01/07/80564.aspx
and then you will probably need to review HTTP uploading protocol and
perhaps troubleshooting:
http://msmvps.com/blogs/dbartosik/archive/category/1921.aspx

You can generate email links where the subject is already filled in, such as
"newsletter subscription request" or some such. Perhaps google for "Mailto
Link Generator" for some possibilities, or just adapt the following to
create your own manually. Use the insert html code fragment:
<a href=mailto:someone@yoursite.com?subject=Newsletter Request>Email Us</a>

Or enter this directly when adding the hyperlink email address:
someone@yoursite.com?subject=Newsletter Request

As per your other question, it appears that a "google mailing list" is
google based, not your website based:
http://groups.google.com/intl/en/googlegroups/tour/index.html?lnk=hptt

DavidF