To send SMS messages with AT commands you use the AT+CMGS
command. It is described in the 27.005 specification. Of all possible AT commands to start working with, it is not the simplest, but it's not impossible either. The important thing is that you MUST wait for "\r\n >" before sending the message content.
The general concept for AT command communication is that you send an AT command line to the modem, and then you MUST read and parse everything sent back from the modem until you receive a Final result code. See this answer for more details. And by all means read the V.250 specification to get a better understanding of AT commands.