What email client do you use?
Perhaps it's worth checking the headers on the sent item email in your mailbox. This should have information on where it was sent (unless BCC'd).
Regarding HOW, could be done via the email provider web interface, or something has haxed your PC and is using your email client to sent out spam. Get a good trojan/virus check, such as Malware Bytes, NOD32, Spybot, etc,etc,etc