yes you are true
as I understand all modems use the serial port for data transmission.
even if the modem connect to your PC with USB. there will be a serial data encapsulated in USB.
just to start
connect your PC to your modem and try to play with some AT commands and see the modem response
you may use serial Port monitor SW to see what's going on the port.
then try to send the same data from your MCU to your modem
Beside connect Tx/RX line as usual serial data transmission, you have to connect all of the modem hardware handshaking lines (RTS, CTS, DSR, DTR, RI and DCD) to MCU.
These lines are RS232 signal and connect to MCU ports via RS232/TTL Voltage Translator Chip such as MAX232.
The handshaking schemes are:
Receving external call
Calling external phone
Terminate connection
RI signalindicating there are external call on modem, normally it is connect to INT request input on MC