How do I insert a mailing list subscription email form in my website?

You'll find detailed form mail script free examples here; they come in different flavours: PHP, ASP, single opt-in. double opt-in, complete form or e-mail only trasmission, etc. They are designed so that integration in your website and links to your newsletter database is easy: add your mailing list management email address, adapt graphic layout with any editor (or insert main forms inside existing pages), upload them to your web server, and you're done.