Old boards with relays that are controlled by transistor switches are an excellent source of ready-made (already calculated) relay modules for Arduino. Below is a photo of the board from the old CRT monitor SAMTRON 56E which is designated as "AN15V(M)1.1".
This board has one relay 12V/5A250V (SDT-S-112LMR) in the kinescope demagnetization circuit (degaussing system) and I found a datasheet for this monitor without much effort, so I did not have to redraw it directly from the board - I just sketched it from there as is.
The relay is controlled by a simple transistor switch with a minimal set of elements (plus a resistor in the collector wire at 47 ohms): a NPN transistor KSC945Y (marked as "C945Y"), a protective diode 1N4148 and a resistor in the base wire for 10 kilohm.
To test this relay module, I used a standard sketch for blinking LED through the 13th pin with a time delay of 1 second, after changing the variable name for this pin and the number of this pin. Everything is very simple here and it does not need a special detailed explanation.
Now, purely for the sake of interest, I will calculate (approximately) the saturation coefficient of the transistor that the engineer chose when designing this section of the scheme.
► 1. The load of the transistor is a relay (SDT-S-112LMR) with a coil resistance of 580 ohms (Rc1) and a resistor with a resistance of 47 ohms (Rc2). Calculate the collector current of the transistor (Ic):