See RS-232 vs. TTL Serial Communication :
https://www.sparkfun.com/tutorials/215Traditional RS-232 is -3v... -25 (but typically -12v or less) for a digital 1 and 0v or above 0v for digital 0. TTL RS-320 is 0v for digital 0, a voltage above some threshold (ex. 1v) for digital 1.
That's one of the reasons computer power supplies still have -12v, after dropping -5v years ago (which was used in ISA slots, and often used on dial-up modems and sound card opamps) but most power supplies don't really regulate it well, you'll often see the voltage between -8v and -12v and it's not a problem.
As the article above shows, you can use chips like MAX232 which have a built in charge pump regulators that produce approx. -10v and +10v from 5v you input.
You can get double voltage or invert voltage with simple charge pump regulators, which work well for low currents (20mA...100mA) :
https://www.digikey.com/short/pm5th7Alternatively, for higher currents you can use switching regulators but these require more components (inductor, resistors etc) around them ... a cheap example is MC34063 :
https://www.digikey.com/short/pm5thdDave even made a video about this regulator:
If you can power your circuit from mains voltage, you can use a power transformer with two secondary windings (and you can connect the windings in the middle and that's your center tap) or a big winding with a center tap. The center tap becomes your ground and the remaining two wires are your positive and negative voltages, after you place a diode and a capacitor on each.
Attached is an example of a positive and negative power supply using a center tap transformer. The LM317 and LM337 are adjustable positive and negative linear regulators. If you don't need to adjust, you can replace them with fixed output linear regulators, for example 7805 or 7809 for +5v or +9v and 7905 or 7909 for -5v or -9v (-9v is way above -3v and close enough to -10..-12v that it should be very compatible with devices that use regular classic RS-232)