How to use SMTP to send mail to some host?

I'm trying to use SMTP to send mail to my account on some server (say, on Gmail).

So far I've tried:

220 mx.google.com ESMTP y14sm3079810ibf.45
HELO
250 mx.google.com at your service
STARTTLS
220 2.0.0 Ready to start TLS
AUTH LOGIN
Connection closed by foreign host.

What am I doing wrong, and how can I fix it so I send an email as though I were my own server?

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