I don’t log the AT commands used for sending, or useful steps along the way.
If you’re a programmer, I can refer you to Lua and Linux shell scripts I wrote for sending SMSs.
In the meantime, this old Siemens SMS PDU guide will explain much:
http://www.alternative-technology.de/sms_pdumode.pdf
You can ignore any security warnings about downloading it, I’ve checked that it’s the original document.