Since a PC is the "terminal", so the CPx is the data communications equipment, DCE. A standard straight-through RS-232 cable is used from a computer or USB-to-serial-converter, to the unit.
We use dumb data terminal programs like TeraTerm and HyperTerm *ALL* the time, in exactly the manner you describe. The command set has it's origins in the old LX200 textual command set, so it is easy to issue them manually for diagnostic purposes. The command set is published on the AP web-site. However, examples of commands I use regularly to determine if a unit is alive, "reachable", and that I am even using the correct comm port in the computer, include "read version" :V# (three characters), and "read local time" :GL# (4 characters). You'll want the terminal emulator "local echo" enabled as the CPx does not "echo".
The moment you power up the unit, it will transmit a single character, "1". That way you know the unit is powered and the embedded software is actually trying to doing something. This may be the single most powerful diagnostic feature. The serial communication parameters are also published on the AP website. But to summarize here for ease in setting up the terminal emulator:
9600 baud, No Parity, 8 bits, 1 stop bit, No handshake. Occasionally, folks "complain" about the lack of parity, but the serial interface remains the most reliable by far.