Having seen the guide, I don't think sending a signal is what I need.
Here is the basic situation:
User A launches a process.
User B is logged in to the same system and needs to access the process to give it a command (what the script is for). Acceptable commands are start, stop, pause, and kill, kill ending the process entirely, while the other commands give it specific instructions.
Although from the format of your answer, it sounds like this should work:
User A starts seeing this:
prompt>
User A starts the process:
prompt> <process>
User A gives any of the aforementioned commands to the process:
prompt/process> <command>
It sounds as though your process is going to have to have a signal handler so that the user B can send various signals (note that a signal handler can do whatever it likes when it receives any signal except SIGKILL(9) or you could implement a "management" shell that user B can log into and issue commands to the process on.