Thank you for your reply.
Yes I clearly misread the tutorial when it comes to powering the driver chip. Just to repeat this once again the logic power comes from Arduino's 5V pin and an external power supply with 3-9V output voltage is required to be connected to the driver chip's VCC pin to provide the motor power.
Is it good to use an AC/DC transformer with the right output voltage? In this case for example 6V 1A or 9V 1A or is that enough power for the pump.
What happens to the motor power supply if a malfunction in the pump occurs and it begins to take more current, is there a possible risk for electric shock from transformer then. Would it be safer to use a large 9V battery to power the pump? The downside of course would be that the battery needs to be recharged from time to time and it would provide power only for short periods of time.
I will be posting my wiring diagram here later before I continue my project just to be sure it is right.