The incoming data to move the servos are generated by Max MSP
Do you have any documentation describing the format of the serial data?
You can have very simple serial communications where each individual character is an instruction.
For example you might just send the characters '0'....'9' and, depending on what character was sent you could do one of the 10 options.
You can have more complex communications protocols where you send strings of characters that need to be parsed to determine the meaning of the message.
I suggest you try practicing sending characters to your arduino.