I built a mains power supply into the unit. But if you're not proficient in safe mains wiring, or doing so isn't legal in your location, buy a ready-made regulated 12 volt DC supply, and plug your stations into the low voltage side of it. All aspects of mains wiring needs to be mechanically strong, and electrically safe.
Each station only uses about 10mA of current, so multiply that by the number of stations, then add a bit extra as spare, to work out how big your power supply would need to be. e.g. Six stations would use 60mA, and a 100mA power supply would give you plenty of spare current, should you want to add any more stations, in the future. You can use power supplies capable of providing more current, such as a 1 amp supply, the intercom stations will only draw as much current as they need.
It's supplying the right voltage that's more critical. Much less than 12 volts, and it won't work very well (9 volts seems to work reasonably well). But if you go over 12 volts, you'll blow up the LM386 audio power amplifier IC, some variations of the IC have a 12 volt limit. Use a regulated power supply, not an unregulated plug pack (where the voltage can go dramatically higher than you'd expect, when it's not supplying a lot of current). Or, you'll need to put 12 volt regulators into each intercom station, and supply them with 15 to 20 volts (series/shunt regulators need a higher input voltage than what they output).
Some voltage regulators are noisy, and will make your intercom audio noisier. For instance a LM7812 regulator is noiser than a LM317 regulator, and switchmode regulators are even noiser, still.
Avoid ground loops by keeping the intercom wiring completely separate from other equipment. Running all the intercoms from a common supply, rather than powering them from camera equipment, makes this a lot easier.
It's usually necessary to connect the intercom to mains ground to kill buzz and RF pick-up. This should only be done in one place, such as in the intercom power supply. However, directly connecting it can cause noise, in itself. Connecting the supply ground to mains ground through a resistor and capacitor is usually sufficient to kill off noise without creating a ground loop.
If you are connecting the intercom to other equipment, such as an audio feed for the program monitor, that introduces another ground into the equation. You could use that equipment to ground the intercom instead of its power supply. Or use an audio transformer on the audio feed input, from a balanced source, and connecting audio ground to the chassis, but not the electronics.