With Python, it depends on your web hosting. Some shared web hosts do PHP and then only do Perl/Python (and Ruby etc.) through CGI. With Python, you can build web stuff either using the CGI model or - if you have hosting that supports it - WSGI. If you are going to do Python and CGI, just look in the documentation for the cgi module. Alternatively, use web.py. You basically need to read in the input as an HTTP POST message on a particular URI. The web.py documentation should describe how to write this.
For the parsing - depends on what format it is being sent as. You can use x-www-form-encoded to transmit simple key-value pairs. I don't know the intricacies of web.py (I use Ruby mostly), but it should basically provide you with a way of getting a 'request' object, doing something with it and then you modify a 'return' object which contains what goes back to the browser. With web.py, this is web.input() - see here.
For anything more complicated, you need to basically POST the data in your chosen format - XML, JSON, magical binary blob format. How you parse that depends on what it is. Simply Google for "python xml" or "python json" or whatever and you'll find the latest library for it.
Inserting into the database - use the mysqldb library for Python (I use Postgres, mostly from Ruby and Java, so I'm not fully hip to the latest Python MySQL libraries).
For sending e-mail, you can either just use sendmail (on Unix systems with a sendmail installation) or you can use Python's smtplib to send it to an SMTP server - if you are just doing admin e-mails, use something like a Gmail account as your SMTP server as you know that it is going to work. Oh, web.py makes it easy - it has a built-in mail module. Use that, I guess.
You probably need to think about security - that means authentication and it means form validation. RTFM for whatever language and database library you use so you don't open yourself up to SQL injection - and do the same for e-mail. You don't want to be a proxy for spam.