How to build a button-pressing machine

Hello everyone,

I want to build a button-pressing machine similar to the one depicted in this video:

What element should I be looking for and can I complete it with arduino?

Thanks in advance

That video shows a linear solenoid. You will need a power supply capable of supplying the rated voltage and current for the solenoid, a solenoid driver and controller. An Arduino output pin cannot supply enough current to drive a solenoid so an external circuit must be used. That can be a transistor with a flyback diode (see the linked page). The controller can be an Arduino or a simple 555 timer circuit.