I'd like to connect a 12V access control device to the Arduino, but I lack the understanding.
How can the signals from and to the device be done when they have different voltages?
I am afraid that the 12V would brick the Arduino.
You could use an opto-coupler:
An opto-isolator (also called an optocoupler, photocoupler, or optical isolator) is an electronic component that transfers electrical signals between two isolated circuits by using light. Opto-isolators prevent high voltages from affecting the system receiving the signal. Commercially available opto-isolators withstand input-to-output voltages up to 10 kV and voltage transients with speeds up to 25 kV/μs.
A common type of opto-isolator consists of an LED and a phototransistor in the same opaque package. Other types of source-sensor combinations include LED-photodiode, LED-LASCR, and lamp-photoresistor pairs. Usually opto-isolators transfer digital (on-off) signals, but some techniques allow them to be used with analog signals.
Here is an example schematic and packaging:
If you have a heavy load (although this does not seem to be your case) then they can also be used in conjunction with relays - here is an eight channel opto-coupler relay module board: