I need to know how exactly does the MK 108 work. I need to make a presentation and I need more detail as to how it operates.
Sound like you want us to make your school assignment 
Since there are only 4 parts in this kit, the operation is very simple.
T1 is a very high gain transistor.
A small base current can drive the transistor enough so that the buzzer sounds.
As you can see, the base current path is interrupted so the buzzer does not sound continuously.
Since water is conductive, it closes the path and the buzzer sounds.