The question you linked to has the information you need to access the modem. You might also find this SO answer helpful for accessing the modem. Be warned that the device file you need to use is different for each model of phone, so you'll have to examine
/dev on each device to find out which file to use.
As it points out, you need to be root to do this. The rooting process is different for each model of phone. For most models, you have to wipe the phone to achieve it, as the process involves unlocking the bootloader (and maybe flashing a custom recovery) in order to flash the
su binary into the system image. Some models have security vulnerabilities you can exploit with a program you download, to achieve this without unlocking the bootloader. How do I root my Android device? explains more about the process, and has an index of questions about rooting particular devices.