A decent mailing list manager is GNU Mailman, which is free. You can
get more information at [ http://www.list.org/ ].
To see an implementation of this, look at [
http://www.politechbot.com/info/subscribe/ ]. Use your "view page as
source" option in your web browser to see how this is implemented
inside of the web page. From what I saw, it looks pretty simple to set
up. Also, be aware that Politech is a VERY high traffic list with many
subscribers, so this solution should probably scale well.
Another free mailing list software page can be found at [
http://www.greatcircle.com/majordomo/ ]. Majordomo was once the
standard by which I personally managed a number of lists, though it
looks like Mailman may be better at this point in time.
Some other software would be:
LISTSERV -- this was once the gold standard. This is not freeware, but
for small mailing lists, you can use the product for free.
[ http://www.lsoft.com/products/default.asp?item=listserv ]
[ http://www.developerfocus.com/projects/ezmeister/ ]
Finally, here's a list of many types of mailing list software
products, not all of them free.
[ http://www.spamliquidator.com/directory/mailing-list-software.html ]
"mailing list software" + "open source"
I hope this helps!