You CAN in some circumstances plug the output directly into your arduino while running from 12v. You can use one of the probes that ties a sense line to ground, put a diode facing the sensor, and when it triggers, with a pullup on the electronics, it will be pulled down - meaning you can use the sensors at whatever voltage they want.
Edit: ah, he shows that.
Also I strongly recommend anyone that want good results to stay away from the cheapest china crap. I spend 20 Euro for Omron and it is definitely make difference. Also when picking a sensor you should know that they are rated for Iron and for aluminium you should divide the distance by two in most cases. This means 4mm probe will sense from around 2mm aluminium.