What relay to put to operate the fan in the bathroom?

On the coil, connect the phase from the lighting. Through normally open, connect the phase to the second speed, and through normally closed - connect the phase to the first speed.

When the light is off, the coil is de-energized, normally-closed contacts are in the closed position - the first speed is working, and when you turn on the light, voltage is applied to the coil and a normally-open pair of contacts is closed and through it the phase is switched on to the second speed. It should work, and then you need to look at the circuit of a specific fan and how the speed switches there. If the bends from the winding (which is most likely), then the above will work.

For example, a relay (the first thing that came across in the store) suits AsKo LY2 10A AC-220V - look, it even has a diagram on the front side. Normally closed contacts are those that remain closed until voltage is applied to the coil, open - on the contrary. There is also IEK REK77 / 3 10A 220V - there are generally 3 pairs of contacts.